Just after seven o’clock on a winter evening, at the end of a long day in which he has returned to his old life of being the second best tennis player in the world, Andy Murray stretches out on a sofa at Queen’s Club in London. It’s cold and dark outside but Murray, despite having practised hard at Wimbledon and now facing an hour of questions, is in a relaxed and sunny mood. He only seems taken aback by the simple passing of time since becoming a father this month.

“The thing that has surprised me most is how quickly everything changes – from the first day she was born,” Murray says of his daughter Sophia. “You don’t notice it when you’re there every day but you look back at a photo on the day she was born to one taken five days later to now, a few weeks on, and you see how much things change on a daily basis.”

The 28-year-old Murray has been a father for only three weeks. His wife Kim gave birth to their daughter on 7 February. Exactly one week before that life-changing Sunday morning, Murray had lost to the world’s dominant player, Novak Djokovic, in the final of the Australian Open.

He reached a fifth Australian final despite concerns about his pregnant wife and the health of her father, Nigel Sears, who collapsed in Melbourne while Murray was winning a third-round match. At the same time, he had to accept that defeat to Djokovic, with whom he grew up on the junior tour, marked his 11th loss in their past 12 matches. Murray has still to add to his two grand slam titles – the 2012 US Open and Wimbledon a year later.

Two and a half years without a grand slam, amid the imperious march of Djokovic, who has won 11 of the blighters, does not seem like a crisis. Murray is still world No2 and this week he returns to competition for the first time since becoming a father. On Friday he will lead Great Britain’s defence of the Davis Cup they lifted so unforgettably in November – when Murray played with such grit and emotion to win all three of his matches in the final against Belgium.

They face Japan in Birmingham and Murray is again expected to win every match he plays – including a crucial singles against Kei Nishikori, the world No6.

There is regret at the thought of being away from home for the first time since Sophia’s birth. “I really don’t want to miss seeing those changes,” he says. “Even when I’m away for a day I feel bad. I feel I should be there and I want to be there as much as I can. So when I’m leaving the house at eight in the morning and getting back at eight at night, I feel bad.”

Murray is part of the Great Britain team preparing to face Japan as they begin their Davis Cup defence. Photograph: Tom Jenkins/The Guardian

It will be closer to 10 by the time Murray gets home on the day we meet but he has already made me laugh when describing how nervously his brother held Sophia the first time he met her. He offers an amusing imitation of Uncle Jamie’s uncertainty when entering the strange new world of babies. Did Murray also worry about dropping his daughter the first time he gathered her in his arms?

“I was OK holding her. The only thing I found difficult was changing her because you see a small person and you think they’re so fragile – or that their hands are so small that when you’re putting their fingers through their top that they could maybe break. But when you see all the midwives – and Kim has a good friend who is a midwife – they’re a lot rougher and they do things much more quickly. Lots of people have told me babies are a lot more resilient than you think. They’re not going to break.”

Has he reached the stage when, changing a stinky nappy, he can hold the baby’s legs as if handling a trussed-up chicken? “I’ve not held her upside down yet,” Murray says, grinning. “But, yeah, after the first couple of days I felt much more confident.”

The key question on court will be whether, just like Djokovic and Roger Federer have seemed to play even better since becoming dads, fatherhood might help his tennis. “It’s tough to tell,” Murray says. “I’ve been training again and certainly haven’t been worse. I’ve been very motivated in practice. Obviously with Novak and Roger it’s worked out well. I don’t know if having kids has made them play better or if they’re just really good.”

Murray smiles again, a little ruefully. “For other players it hasn’t worked out as well. But [fatherhood] is a positive thing – and tennis not being your priority can help. It lends perspective when you have a bad loss or bad practice. The outcome of a match is not everything but I want my daughter to be proud of her dad when she grows up and sees what I did. I hope it works out in a positive way on the court but if it doesn’t, it’s not the end of the world.”

I’ve not won a slam for a couple of years I don’t know if I’ll win another one

There is so much steel in Murray, for he plays with the fierce heart of the boxers he admires, that his appetite for hard work and victory is unlikely to be diminished. Great sportsmen often galvanise themselves at turning points in their lives.

It’s different when an ageing athlete hits the crossroads and, as time closes in, the old intensity withers away. But settling into a permanent relationship, or becoming a father, alters the focus of the burningly ambitious tyro. In its place, something more layered can help produce a new kind of fire. It might be less raging – but a deeper sense of control and experience can produce lasting greatness.

Here, there is a sense that Murray is merely pausing before returning to a sapping battle with fresh purpose. Last week it was 10 years exactly since he won his first ATP title when, aged 18, he beat Lleyton Hewitt in San Jose. It was striking Murray won the tournament on his own, with no backup team around him and, also, because he revealed to the world for the first time he had a girlfriend. Does he remember any concern that kissing Kim at courtside would start the invasive scrutiny that has since punctuated his life?

“I was 18 so I really had no idea. I didn’t know what that side of things would be like.”

Murray is both nostalgic and understanding when remembering the difficulties of more anonymous times. “Mark Petchey was my coach but he wasn’t in San Jose. He came out the following week when I went straight to a tournament in Memphis. Kim went home and Mark came out. I only travelled with Mark in those days. That was the team – me and Mark. He coached me for nine months and Mark is one of the best coaches I’ve had.

“I loved working with him. But one of our mistakes was that I didn’t have a place in London and so I would stay with him and his family. I got on great with everyone and loved the kids – he had two young girls – and I stayed upstairs in the attic. I loved that. They really took me into their family but we were living with each other and it was just me and him on the road all the time. We spent breakfast, lunch and dinner together and worked with each other in-between.

“It’s very difficult for the coach because he’s having to hang out with an 18-year-old and also be a father figure. At that age I still needed to make sure I had my shoes in my bag and my strings in my racket, and [I was] warming up and getting to sleep at the right time. Mark was great at all that but we just spent too much time together.”

He now has a proper team around him but, being Murray, it is also more interesting than most because his head coach is a woman. Amélie Mauresmo got the job in June 2014. It generated scepticism at the time but 2015 marked his most consistent year on tour. Even Mauresmo becoming a mother last August has not undermined Murray’s progress.

“Amélie started with me at a tough time,” Murray says. “I’d just dropped out of the top 10. I’d had my [back] surgery at the end of the previous year and it was a tough road back. But from No11, with her I managed to get up to No2, and challenging for slams again. The depth we go into when we discuss the matches has been higher than with other coaches. When she played against Venus and Serena Williams, who are very powerful, she won in different ways – coming to the net, using more variety, lots of spin. She has encouraged me to do that and it’s something I did when I was much younger. She’s also committed. Amélie’s spent a lot of time with me since becoming a mother and that continuity helps.”

Murray says his coach Amélie Mauresmo has encouraged him to add more variety to his game. Photograph: BPI/Rex Shutterstock

Murray is probably the deepest thinker on the men’s tour and he and Mauresmo will talk in a way that transcends the usual sporting platitudes and stats when they try to find a way for him to beat Djokovic again. He picks up on a misleading statistic which suggests he made only 28 unforced errors in an epic five-set win over Milos Raonic in the Australian semi-final – but that 65 unforced errors apparently flew from his racket in the three-set final. “The rallies are much shorter against Raonic. If you make a mistake after a 30-shot rally as a player you don’t go: ‘Oh, that’s an unforced error.’ Djokovic makes more balls and he’s consistent. So you have to be more aggressive and take more chances.”

A delicate balance is required because increased aggression can lead to diminished consistency. “Exactly. A lot of commentators say you have to be more aggressive. Does that mean you hit the ball harder or play closer to the line or serve and volley? Does it mean you have to stand closer to the baseline? At the highest level you can’t just say: ‘Be aggressive.’ You need a proper strategy. José Mourinho wouldn’t send his team out against Barcelona and just say: ‘Be more aggressive.’ It’s a lot more complex playing the best in the world.

“Floyd Mayweather is a good example. A lot of people say: ‘Just fight him how Oscar De La Hoya fought him. Back him up and throw a lot of punches when he’s on the ropes.’ But when you’re in the ring it’s much more difficult to do that.”

It also becomes harder when, as in Melbourne, Murray starts slowly and loses the first set 6-1. Murray tends to beat Djokovic, who leads their head-to-head record 22-9, when he wins the first set. “All of them actually,” he says more precisely of the nine victories over his nemesis.

It must be crushing, psychologically, whenever he drops the first set to Djokovic? “No. I obviously lost the first set 6-1 but the next two sets were close. If it was 7-6, 6-3, 6-1 then it would be like ‘Oh, God.’ But, yeah, if the top players win the first set they’re winning 95% of the time. It helps to get a lead and then play with more freedom. I had break-points in his first two service games but I still went 3-0 down. He played very well for the next 30 minutes and my level dipped.”

Murray shakes his head defiantly when asked if he is haunted by winning only one out of their last dozen matches – in Montreal last August. “I don’t look as much into that as everyone else. Look at [Stan] Warwinka winning his second slam [in Paris last year] against Novak. He’d lost to him 13 times in a row. I don’t think he’d ever beaten [Rafael] Nadal [in 12 previous meetings] when Stan won Australia in 2014. Each time you step on to the court it’s a completely new match. The reason Novak’s beaten me a lot recently is that he’s been the better player. But if I play him tomorrow it’s a bit like roulette. People think there have been five reds in a row. It’s got to be black next time – but the roulette wheel doesn’t know what’s happened before.

You need a proper strategy. Mourinho wouldn’t send his team out against Barcelona and just say: ‘Be more aggressive.’

“Obviously tennis is different because skill is involved but when we play tomorrow the match in Australia doesn’t mean he beats me the next time. Just like after I beat him in Montreal it didn’t automatically mean I would beat him the next time.”

Djokovic’s grip on men’s tennis during the last two years has been so firm I ask Murray an unfair question. Could his rival overtake Federer’s record of 17 grand slam victories? “It’s tough. A few years ago everyone thought Nadal would pass it. If Novak keeps going at the rate he’s going now he finishes on about 23 slams. But to predict someone is going to win that many?

“Look at Serena. At the US Open she was in the semis and it was considered a certainty she would win. It didn’t happen. Same as in Australia [where Williams lost to Angelique Kerber]. Winning more helps but when you’re trying to achieve something that’s never been done before, the pressure builds. Novak has the potential to do it … but it becomes harder. Tiger Woods was nailed on to pass Jack Nicklaus’s major wins but there are no guarantees.”

More simply, will Murray win a few more slams in his own career? “I don’t know. When I lost the Wimbledon 2012 final I didn’t know if I’d ever win a slam. Then when I won the US Open they were asking: ‘What’s going to happen now?’ I thought: ‘It’s taken me this long to win one I don’t know if I’ll win another.’ And now that I’ve not won one for a couple of years I don’t know if I’ll win another one.”

This is not an admission of defeat – for there is another flash of Murray steel when he looks up and says: “But I believe I still can. I’ve been close the last year. I had my best French Open. At Wimbledon I was playing extremely well and it took Federer to play an unbelievable match. He served 79% first serves which might happen once a year – twice at best. I can definitely still win more slams. I’ve just got to take the chances when they come.”

Murray was overcome with emotion after winning the Davis Cup with Great Britain last year. Photograph: Andrew Milligan/PA

Murray’s belief is bolstered in the familiar surrounds of Queen’s. This summer he will attempt to win the Aegon Championship for a record fifth time and he talks with real ardour about his desire to lift the trophy of the tournament he loves most outside the four grand slams. Should he be successful at Queen’s Murray will overtake a group of four-times winners who include Roy Emerson, John McEnroe, Boris Becker, Lleyton Hewitt and Andy Roddick.

He will also be rejuvenated by making his comeback, as a father, in the Davis Cup – a team format that means so much to him. What was he thinking, after winning his reverse singles with a sumptuous lob against David Goffin that sealed a 3-1 win over Belgium, when he fell on to his back and the tears came? “Just disbelief that you’d won the Davis Cup. And then everyone jumped on me. I don’t like it because I get a bit claustrophobic. I’ve also never liked it when I’m watching a big match and a player wins but doesn’t shake hands with the opponent. I wanted to say bad luck to the Belgian team first before celebrating.”

Did the captain, Leon Smith, need to do much persuading before Murray decided to play this week? “No. I always wanted to play providing everything went well with Kim and the baby. It’s going to be a tough tie. Last year the toughest team we played was France and they didn’t have anyone ranked as high as Nishikori. He’s capable of winning two singles.

“I lost to him once at the World Tour Finals in 2014. We’ve played six times so I’ve won five. But he’s one of the best players in the world and I won’t have played a match for almost five weeks. That’s the longest break I’ve ever had at this stage of the season. There are no guarantees but hopefully I can play well and help the team win.”

His usual involvement in the doubles with his brother “depends on how the singles go on the first day. When you haven’t played for a long time things hurt a bit more after a match”.

‘The only times I get nervous is watching a really big fight or when my brother is playing. I get to the stage where I’m actually shaking.’ Photograph: Tom Jenkins/The Guardian

Murray stresses he is as hungry as ever and he feels ready to play at this level for many more years. “Definitely. Andre Agassi was one of the few guys in the last 20 years who played at the top of his game until he was 36. But Roger is 35 this year. David Ferrer is 34 this year and Feliciano López turns [35]. Roger’s in the top three in the world, Ferrer’s in the top 10 and López is around the top 20. It all just depends on how my body handles it.”

There is still enough time for Murray to extol the courage of the fighters he loves and to discuss the Frampton-Quigg bout last weekend. “Boxers risk a lot in the ring. That’s one of the things that attracts me to it. You want to see a knockout but I also really don’t want to see people get hurt. It’s this constant dilemma when I’m watching boxing. The only times I get nervous is watching a really big fight or when my brother is playing. I get to the stage where I’m actually shaking.

“It’s that strange. But the thing I really like about boxing is that, at the end, they respect each other. I find that amazing because sometimes before a fight it gets a little too much. They can do that to each other and put themselves through so much pain and then, at the final bell, they show such respect.”

Murray also passes on some of the lessons he has learnt from other great sporting figures like Sir Alex Ferguson. “He talked about the three Cs … consistency, concentration and confidence. But most of the time I just bombarded him with questions like who was better? Messi or Ronaldo?”

The new dad laughs at himself but it will be a surprise if Murray does not strive harder than ever to lift his own trio of Cs to an even higher level in the next few years. Consistency, concentration and confidence may pour out of him as, content and fulfilled at home, he returns to battle in the gladiatorial setting of the tennis court. The next stage, for Murray and the rest of us, promises to be even more gripping than the last decade.

Andy Murray looks at the Queen’s singles trophy he has won four times. Photograph: Tom Jenkins/The Guardian

Andy Murray, Rafael Nadal and Stan Wawrinka will compete in the 2016 Aegon Championships at Queen’s Club, 13-19 June

• This article was corrected on 1 March 2016 to reflect the fact that there was one week, not two, between the Australian Open final and the birth of Andy Murray’s daughter