Johanna Konta could be the last of eight British players left in this Australian Open by the weekend, but she views her second-round match against Garbiñe Muguruza on Thursday with the same equanimity as she would an opponent from outside the top 100.

Having lost to too many outsiders in big tournaments in the past, she is aware that danger lurks in every match. Her memories of Muguruza are clear and largely encouraging, however.

The only time Muguruza beat Konta was in qualifying in Luxembourg seven years ago, when both were still searching for their identity on Tour. When it mattered, Konta got the better of her on the grass of Eastbourne in a seaside stroll in 2015, not far from her home, then prevailed on a wickedly hot day at Flushing Meadows a couple of months later to tip the Spaniard out of the US Open in three long sets.

Muguruza, two years younger at 25 and 20 places above Konta in the rankings at 18, has the better record (six WTA titles, including two majors, to three and none) and has won more money ($18.2m to $7.2m), but she is beatable, even on the big stage, where nerves have often kicked in.

Here Muguruza made it on to Court No 3 on Tuesday to account for Zheng Saisai, 6-2, 6-3, in an hour and a quarter. She said later: “It’s never easy, first round. I didn’t know a lot about my opponent, because this is the first time we played each other.”

If that smacked of complacency, there will be no room for it against Konta, who goes in battle-hardened after taking nearly three hours to beat the combative Australian Ajla Tomljanovic in serious heat on Court No 3.

Muguruza definitely remembers their match in New York, describing it as, “a tough second round. She can play very well.” Asked was she surprised that Konta has yo-yoed on the rankings, she said: “No, it’s just tennis.” Aggressive players, she observed, “have good moments and not so good moments”.

Konta says of Muguruza: “If I have learned anything in the years I have been on Tour, it is anybody can play at the very highest level on any given day. And for someone to win two grand slam titles, still ranked in the top 20, she is a heck of a player.

“ Going on court against anyone, you don’t underestimate them, especially not someone like her. No I don’t think she is vulnerable – I think she is doing very well and I am looking forward to playing her again.”

Pleasantries aside, Muguruza had by far the easier route to the second round. The prize for both is a probable path to at least the quarter-finals where the likely opponent will be Serena Williams, who could hardly have been more imposing in her first match here since winning the title in 2017 when seven weeks pregnant.

The 37-year-old American needs one more major to match Margaret Court’s all-time record of 24, and began her campaign on Tuesday by blitzing her neighbour back in Palm Beach, Tatjana Maria, 6-0, 6-2, in 49 minutes. In the next round she plays the Canadian Eugenie Bouchard who was way too good for the Chinese wildcard Peng Shuai, winning in just under an hour for the loss of three games.

“She lives in the community next to me,” Williams said of Maria. “It’s nice. She’s a really nice person. And her husband is really nice. Her family is sweet.” It was tempting to wonder what she would have done to the German had they not been neighbours.

Serena Williams serves in her first-round match against Tatjana Maria. Photograph: Julian Finney/Getty Images

So, she filled her post-match remarks with platitudes, flatly refusing to talk about her meltdown in the 2018 US Open final in September, which is perhaps understandable. It was more than four months ago.

However, when asked why she had avoided media commitments in a place where she has had so much success and which has always made her welcome (unlike one or two other places on the Tour over the years), she insisted it was to spend more time with her young daughter, Olympia. Sentiment is fine; but she has obligations as well, and sometimes this escapes her understanding.

“That’s the priority for me,” she said. “It’s kind of what I do in Florida. I train and I go right home and I spend the rest of the day with my daughter. For now, as a working mom, I feel guilty. And I understand that’s normal, but these are years I’ll never get back. I just try to spend every moment that I can when I’m not working with her.”

Fair enough, many will say. But she will need to be fully focused once the draw thins out and the opposition improves. Bouchard is determined to provide stiff resistance.

“I have had tough moments the past year, for sure, tough injuries,” said Bouchard, who once was No 5 in the world and last year dipped as low as 194, arriving here ranked 79. “When you lose early, it’s less fun, of course, but I feel like I’m improving.”

Williams says she cares nothing for rankings. “I don’t want to give myself a ranking anymore. It gives me too many negative expectations. I always expect to reach the sky. Anything below it is not good enough for me. I just know that I’m going in the right direction.”