Throughout the past week, as ­Jannik Sinner has taken his first steps toward putting the revelation of his failed doping tests behind him, the Italian has repeated in almost every appearance and ­interview that he is taking things match by match and day by day. He is endeavouring to focus only on the immediate task ahead, ­blocking out all else.

In the process, the world No 1 continues to lay the foundations for a title challenge at the US Open. On Thursday, Sinner navigated a turbulent opening set against a tricky young opponent to reach the third round with a 6-4, 6-0, 6-2 win over Alex Michelsen of the United States.

Last week, Sinner announced his previously undisclosed case had concluded with an independent tribunal ruling that he bore no fault or negligence for the fact that the banned substance clostebol was detected in two anti-doping tests. A few days later, Sinner’s US Open campaign had started with a minor scare as he trailed the American Mackenzie McDonald before recovering emphatically toprogress.

An even greater challenge seemed to await the Italian against Michelsen, a fast-rising 20-year-old. After reaching his third ATP final last week at the Winston Salem Open, the American is now the youngest player inside the top 50 at a career high ranking of No 49.

In that final, which he lost to Lorenzo Sonego of Italy, Michelsen smashed a ball into the crowd in anger, striking a spectator. According to the rules and the precedent set by similar incidents, he should have been defaulted. Instead, he was allowed to play on. While such an incident would usually generate more discussion, Sinner’s anti-doping case has overshadowed all minor talking points and controversies.

As Michelsen stared down the No 1 player at Arthur Ashe Stadium, the opening set was tense and ­competitive, with the two players trading breaks as they struggled to defend their second serves. But Sinner completely outserved his opponent in the decisive moments, which allowed him to narrowly edge out the opening set. With the first set secured, a far more relaxed Sinner began to step inside the baseline and dominate the exchanges as he ­navigated a ­comfortable win.

While he builds momentum on the court, Sinner’s anti-doping case has continued to generate conversation away from it. Despite facing American players in both of his first two matches, he has received a warm reception from the audience. The response from his fellow players has been more mixed, with both support and criticism alike.

“I cannot control the players’ reaction, and if I have something to say to someone, I go there privately, because I’m this kind of person,” he said. “But, look, overall, it has been not bad. So I’m happy about that.”

Discussions about the case itself have also continued. Sinner’s anti-doping rule violation is a rare example of an athlete being able to contest successfully the automatic provisional suspensions that an athlete receives upon notification of testing positive for a banned substance.

His team moved incredibly quickly, contesting the first provisional ban on the same day, 4 April, he received the notification and before it was repealed a day later. For many, it underlines the benefit of having money, clout and a team of professionals around him. In the aftermath of testing positive, some lower-ranked players would probably be scrambling for lawyers and representation and would not be in a position to respond so quickly.

After his previous match, Daniil Medvedev noted that what concerned him most about anti-doping was being found positive for a banned substance without knowing the origin. Sinner was able to quickly determine that he had been contaminated by an ointment purchased by his fitness trainer Umberto Ferrara, which is often not the case.

Medvedev said: “For me the only thing where I’m a little bit, like, ­doping cases make me scared is imagine – so he knew what happened, and good for him, so he managed to defend himself. Imagine whatever tennis player in the top 100 gets an email, and they say: ‘Look, there was cocaine in your blood.’

“You come to them and you say: ‘Well, I never did anything in my life. I don’t know how did it get there.’ When you don’t know, you get suspended. That’s a little bit the tricky part, but that’s how doping rules are.”

As he continues to navigate this situation, Sinner continues to win. His win-loss record now stands at a tour-leading 50-5 (91%) and he has won his past six matches, after winning his fifth title of the year in Cincinnati last week. He will face Christopher O’Connell in the third round after the Australian defeated Sinner’s compatriot Mattia Bellucci 6-3, 6-4, 3-6, 6-3.