Newly blonde but an established, familiar figure among the ivy and the petunias of south-west London: less than four months after leaving her teens, Coco Gauff has the air of a lawn tennis elder.

There’s a feeling that this could end up being a very big Fortnight for the 20-year-old at the All England Club, a view possibly shared by Roger Federer’s parents Robbie and Lynette, and even his twin sons Leo and Lenny, who were in the No.1 Court crowd for the American’s 6-2, 6-1 victory over Romanian qualifier Anca Todoni in the second round.

Two generations of Federers looking on felt like some kind of endorsement for the US Open champion, who has reached the last 32 for the loss of just six games.

Gauff has been associated with these grass courts since her breakthrough as a 15-year-old qualifier. She’s playing Wimbledon for the fifth time (and but for the pandemic this would be her sixth Championships).

And the one-sided nature of her first two appearances – there were moments in this match when she felt as though she could have played cleaner tennis but she was generally happy – suggest that she could be about to venture very deep into the Wimbledon draw for the first time, maybe even go on to lift the Venus Rosewater Dish, to add to the US Open trophy she hoisted in New York City last September for her maiden Grand Slam title.

Playing on No.1 Court is always “special” for Gauff, she noted, as this is where it all started for her with a victory over Venus Williams in the opening round of The Championships 2019.

In the five years since Gauff broke through at Wimbledon that summer – she went on to reach the last 16 – she has won a US Open title, played in a Roland-Garros final and reached the last four of the Australian Open. What she hasn’t done since then is go any further into a Wimbledon draw, though she did match her 2019 run by also making the fourth round in 2021.

Last summer Gauff lost to a qualifier in the opening round, which put her in “a dark place”. But she has been learning about life over the last 12 months, which has included recognising that there’s no need to be consumed or overwhelmed by expectation and pressure.

Ultimately, playing tennis is a game, something to be enjoyed rather than endured.

There are a couple of other reasons why Gauff could be well placed this summer. Significantly, she’s playing her first Wimbledon as a Grand Slam champion, so understands what it takes to win seven matches over two weeks. She’s also ranked at a career high of No. 2.

It’s now 20 years since a teenager last won the ladies’ singles title on the Wimbledon grass. That was Maria Sharapova, who was just 17 when she surprised Serena Williams in the 2004 final. Wimbledon won’t have a teenage champion this summer either. But the tournament could have something close: a lawn tennis elder who's just 20 and a third.