Most tennis players dream of winning a grand slam title, very few get anywhere close. At the age of 21, Naomi Osaka has two grand slam titles and when she wakes up on Monday morning, she will find No 1 next to her name on the world ranking list. It does not get much better than this.

Yet it could do, quickly. Osaka’s 7-6, 5-7, 6-4 victory over Petra Kvitova in an outstanding final at the Australian Open not only sealed her place at the top of the game but also proved her win at the US Open was no flash in the pan. Though Serena Williams, whom she beat in New York, will continue to chase the two grand slam titles she needs to break the all-time record of 24, Osaka is well-placed to usurp her as the biggest player in the sport.

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Consider the facts. Osaka is the first woman to win consecutive grand slam titles since Williams in 2015. She is the first woman to follow her maiden grand slam title by winning the next one since Jennifer Capriati in 2001. Going into 2018, she had not won a title and was ranked 72. In the space of 10 months she has won three big tournaments, Indian Wells, the US Open and the Australian Open.

Consistent, powerful, a superb athlete and with an ability to find inner calm under pressure, she has everything required to stay at the top. However, just a couple of hours after her victory here Osaka said she felt her success had been a long time coming.

“In my mind, I would have liked to win this tournament last year, and I still have nightmares about a forehand I hit against [Simona] Halep when I had break point and I hit it out,” she said.

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“She went to the final after I lost to her. In the French Open, I played against [Madison] Keys and she went to the semis. I feel like every match I play, I have chances, so it always haunts me. If you are talking about if I thought I would win another grand slam before the US Open, I think possibly Wimbledon, I would have thought I had a chance, but then [Angelique] Kerber destroyed me. It just felt like learning experiences.”

She has learned fast. The $2.95m she picked up for winning in Melbourne takes her career earnings through the $10m mark but her off-court earnings are likely to dwarf those in the years to come. Osaka had already signed four sponsorship deals since the US Open and, with her stock rising even more, the Japanese market alone will be hugely lucrative.

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Osaka will fly back to Florida this week where she can catch up with her family, including her sister Mari, also a tennis player. The French Open and Wimbledon will soon be on the agenda, though, and Osaka feels she can excel on any surface.

“I have always felt like I could maybe be an all-court player,” she said. “The first time I played all the grand slams, I got to the third round in all of them. I had one disappointing grand slam [losing in the first round at the French Open]. I think mentally, I don’t like clay. I always tell myself I don’t like clay, so I never really embrace anything about it and that is something I have to change and the same goes for a grass court, because I see people slide and slip and it is a little bit frightening for me, so I think I have to change that.”

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Being the world No 1 comes with added responsibility, the chance to be a leading voice in the women’s game. For now, she is focused on her tennis. “To be in this position feels a bit weird because I feel like, all of my life, I have been chasing people and chasing after the ranking,” she said. “It is a bit strange for me to say it like that, for it to be a leadership position. I know No 1 is very difficult because people expect you to win all the time and you always have really hard matches because everyone wants to beat you. I feel like you should ask me after I have played my first match.”

The way she held her nerve under pressure, both in New York and in Melbourne, suggests she will be able to handle it.