More than 1,000 singles matches into her illustrious tennis career, Serena Williams’s first matchup against Anett Kontaveit — currently the second-ranked women’s player in the world — certainly could be her final one.

It also could turn out to be a major step in what could be one final, magical run at the U.S. Open, perhaps even putting the six-time winner at Flushing Meadows and the 23-time Grand Slam champion in contention to finally match Margaret Court’s elusive all-time record of 24 Grand Slam singles titles before she heads off into expected retirement.

“At this point, honestly, everything is a bonus for me, I feel. I mean, I think every opponent is very difficult. I’ve seen that over the summer. The next one is even more difficult,” the 40-year-old Williams said after improving to an astonishing 857-154 in her 1,011 career singles matches with a straight-sets win Monday night over Danka Kovinic at Arthur Ashe Stadium. “It’s good that I was able to get this under my belt.

“But I’m just thinking about this moment. I think it’s good for me just to live in the moment now.”

Venus Williams said she was unable to attend her younger sister’s latest New York moment in preparation for “an early morning” Tuesday, which turned out to be an afternoon loss in straight sets to Belgium’s Alison Van Uytvanck. The 42-year-old Venus sidestepped a question about her own eventual retirement, pointing to the sisters competing in women’s doubles beginning Thursday. But the elder Williams insisted she has stayed out of Serena’s decision to “evolve away” from the sport the siblings revolutionized.

“I think she’s had some time to process it, and she’s doing it the way she wants to,” Venus Williams said. “That’s what matters most is to do things on her own terms.

“We’re a huge influence on each other, and I’m a huge influence on her. For me, I just kind of felt like my role is to make sure I don’t influence her in any way, and that this decision needs to be all hers and her family’s … I think that’s the role I play is definitely support with everyone else in my family.”

Kontaveit, who only has advanced past the fourth round once in 29 Grand Slam events since 2014, will be across the net Wednesday night looking to spoil the going-away party, with the winner of that match slated to face either Ajla Tomljanovic (ranked 46th in the world) or Evgeniya Rodina (67th) in the third round.

“I’m really excited. I was really rooting for her to win [Monday],” said Kontaveit, the highest-ranked player ever from Estonia. “I’ve never played against her. I mean, this is the last chance. Better late than never.

“But, yeah, really excited. I think the atmosphere is going to be amazing. I’m really looking forward to it. I think it’s going to be one of those matches this year that I haven’t had too many where I just have no pressure on me … I’m really going to enjoy the atmosphere being out there against the greatest player of all time.”

Asked for her favorite memory of watching and learning about Serena growing up, the 26-year-old Kontaveit said, “I think I just remember her always fighting, her always fist-pumping, always being so intense on the court, which I think is great. The matches are so competitive. She’s just always there. She’s always fighting, always giving 100 percent.”

The buzz surrounding Monday’s victory and Wednesday’s second-round match was inescapable throughout Tuesday’s press conferences on the women’s side. Top-seeded Iga Swiatek wouldn’t face either Williams or Kontaveit until the finals, but nine of the 12 questions she was asked following her 6-3, 6-0 first-round victory over Jasmine Paolini were about those two players.

“I can’t imagine what [Williams] must feel, having this kind of atmosphere around her and just finishing — I know she’s doing a tournament, but I feel [Monday] it was, like people did so much work to show appreciation to what she’s done. It’s pretty amazing,” Swiatek said. “I have never seen something like it.

“For sure it was like the most popular first round of a slam ever.”

Imagine what the reaction will be if Williams is able to pull off another victory against a more challenging opponent in the second round.