NEW YORK >> For as long as Serena Williams remains in the U.S. Open bracket, there is one overwhelming question that will hang over the proceedings and help define the moment: Could this be the last chance to watch her play?

The second opportunity for spectators to shower Williams with adoration — and for the 23-time major champion to enjoy that outpouring at what she has hinted, but purposely not definitively declared, will be her final tournament — was scheduled for Wednesday night in Arthur Ashe Stadium, the largest arena in Grand Slam tennis.

The opponent this time: No. 2 seed Anett Kontaveit, a 26-year-old from Estonia whose current ranking is much better than Williams’ is, but whose career resume lacks so much as one quarterfinal victory at any Slam event.

Forget, for a minute, the relative merits of the two players’ skills and styles of play. Forget the X’s and O’s of the matchup. Because this trip to Flushing Meadows is, as always, about the points and the games and the sets and the scores for Williams, who won her first trophy here at age 17 in 1999 and is now 40.

As strident a competitor as tennis, or any sport, has seen, as rightly self-confident in her abilities as an athlete, Williams was not about to think of this whole exercise as merely a farewell tour.

She came to New York wanting to win, of course.

That’s what Williams showed in the first round on Monday, when she got past some early shakiness to beat 80th-ranked Danka Kovinic 6-3, 6-3 in front of a packed house that roared with approval from start to finish. The crowd of more than 23,000 in the stands and thousands of others watching on a video screen outside Ashe helped break the U.S. Open record for largest attendance at a night session.

“I was just thinking, like, ‘Is this for real? Really?’” Williams said about the roars that greeted her entrance for the match, so raucous she “could feel it in my chest.”

“At the same time I’m also thinking, I still have a match to play and I want to be able to play up to this reception, almost. It was so loud. I just was overwhelmed in a good way. But at the same time, it’s like you have to be focused, you have to be laser-focused,” she added. “That’s what I needed to do and that’s what I tried to do.”

Other players who watched from the seats, or on TV, were struck by the scene. One that seemed likely to be repeated on Wednesday.

“For sure, it was like the most popular first round of a Slam, ever. Yeah, it’s just amazing. It shows how much she has changed our sport and how much she has done. I’m pretty happy that she can experience something like that,” said No. 1-ranked Iga Swiatek, a 21-year-old from Poland who owns two French Open titles. “I also feel that not every player would handle that kind of fuss around your first match of the tournament. She’s handling it pretty well, as usual. So that’s just confirmation of how great she is.”

On Wednesday, Williams was expected to don the same glittery crystal-encrusted top and diamond-accented sneakers — replete with solid gold shoelace tags and the word “Queen” on the right one, “Mama” on the left — that she sported Monday. Long someone whose on-court fashion has stood out from the crowd, Williams helped design the Nike combo, which was inspired by what figure skaters wear to compete. Williams’ daughter, Olympia, who turns 5 on Thursday, wore her own version to sit in the stands Monday, along with beads that paid tribute to Mom’s hairstyle when she won the 1999 U.S. Open.

Regardless of how Williams vs. Kontaveit went, there would be more in store for the American, who announced on Aug. 9 she was intent on “evolving” away from her playing days (she said she does not like using the word “retirement”).

Williams will team up with her older sister, Venus, in doubles on Thursday night against the Czech duo of Lucie Hradecka and Linda Noskova. It marks the reunion of a partnership that produced 14 Grand Slam doubles championships but last participated in that event anywhere in 2018.

Venus said it was Serena’s idea to enter the doubles.

“More than anything,” said Venus, who is 42, “I just want to hold my side of the court up and be a good sister.”