NEW YORK — If there were any boos directed Jannik Sinner’s way at the U.S. Open, they were imperceptible amid the polite applause from the sparse crowd at Arthur Ashe Stadium when he was introduced Tuesday before the No. 1-ranked man’s first match since his doping case emerged a week ago.

After a sloppy and slow opening set, Sinner pulled away for a 2-6, 6-2, 6-1, 6-2 victory against Mackie McDonald of the United States to reach the second round at Flushing Meadows.

There were no apparent signs in the stands or disparaging shouts making reference to what no one knew about for months: Sinner tested positive twice for trace amounts of the anabolic steroid Clostebol in an eight-day span in March.

Nothing was announced publicly until last week, when word came that the 23-year-old Italian was docked prize money and ranking points from the tournament where the first result appeared, but he escaped a suspension because it was ruled he was not at fault and the drug entered his system unintentionally, through a massage from his physiotherapist.

In his first public comments on the matter, at a pre-tournament news conference Friday, Sinner said he had fired the fitness trainer who bought an over-the-counter spray containing Clostebol in Italy and the physiotherapist who used it for a cut on his finger before treating the player and transferring the substance to his body.

During a brief on-court interview in Ashe, Sinner wasn’t asked about the case, which has drawn some criticism from other players, including defending champion Novak Djokovic, about the way it was handled and questions about whether certain athletes are treated differently than others when it comes to the process for determining punishments related to doping.

But in an indication of the way the crowd treated him, Sinner offered this observation: “The support is always amazing, so thank everyone for coming, for staying.”

Against McDonald, an American ranked 140th who fell to 4-13 in 2024, Sinner was way off the mark at the outset. He double-faulted. He put what should have been an easy smash into the net. He messed up volleys. It added up to 14 unforced errors in the initial set, helping McDonald grab five games in a row from 2-all to collect that set and go up a break in the second.

“I started a little bit not in the best way. But for sure, the first matches in every tournament, they’re not easy. ... I tried to stay there mentally and get in a rhythm,” Sinner said. “I will try to improve for the next match. For sure, I have room to improve.”

That one will come against another American foe, Alex Michelsen.

In other action Tuesday, top-ranked Iga Swiatek edged Kamilla Rakhimova 6-4, 7-6 (6). The 2022 champion was one point away from being forced to a third set when Rakhimova took a 6-3 lead in the tiebreaker. But Swiatek recovered and won the next five points, finishing the match when her opponent missed a backhand.

Two-time champion Naomi Osaka made an impressive return to the tournament by beating No. 10 Jelena Ostapenko 6-3, 6-2.

Osaka, the 2018 and 2020 champion, needed only 64 minutes to oust Ostapenko, the 2017 French Open champion. It was the kind of performance that was standard from Osaka when she reached No. 1 in the rankings and won four Grand Slam titles between 2018-21.

But she had missed large gaps of time since, first for mental health breaks and then after giving birth, and just this month posted on social media about the struggles of not playing as well as she used to after failing to qualify for the tournament in Cincinnati.

Danielle Collins’ singles career at Grand Slams ended when the No. 11 seed was upset by fellow American Caroline Dolehide 1-6, 7-5, 6-4. Collins, 30, plans to retire at the end of the season. She’s still entered in doubles at Flushing Meadows.

No. 11 Stefanos Tsitsipas and No. 19 Felix Auger-Aliassime were both knocked out, while No. 7 Hubert Hurkacz and No. 25 Jack Draper were among the men’s winners.