NEW YORK -- From the beginning, the trajectory was evident.

When Coco Gauff was 12 years old, she won the 12-under Junior Orange Bowl title, joining Steffi Graf (1981), Monica Seles (1985) and Jennifer Capriati (1986). Between them, those marquee players went on to win 34 Grand Slam singles titles.

Make that 35 -- and counting.

Gauff had already met Serena three times by the time she won the prestigious junior event and trained twice with her coach, Patrick Mouratoglou, in France. Asked about her goals, she replied simply, “I want to be the greatest of all time.”

And while it would be absurd to even suggest it’s likely -- based on this bolt out of the blocks, it’s not an impossible dream.

For several years now, Gauff has been pursued by other people’s increasingly great expectations.

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But this summer, with several huge strides, the 19-year-old American has finally fulfilled them. In a span of 39 days, she has won 18 of 19 matches and, in succession, the three biggest tournaments of her life.

The most recent, the US Open, changes the temperature completely. Saturday’s 2-6, 6-3, 6-2 victory over soon-to-be No.1 Aryna Sabalenka was Gauff’s 12th in a row and completes a remarkable circular story.

Gauff is the first American teenager to win the US Open singles title this century and only the third overall. When Serena Williams did it in 1999, Gauff was still more than four years from being born. Going forward, however, they always will be linked.

“Being in any sentence with her is great,” Gauff said of her idol earlier in the tournament. “It’s something that I’m used to a lot. So I’m not going to sit here and be like, ‘Oh, I’m shocked, but I feel like a lot of the stats have aligned with her, and people find new things to think about.

“I was the first teenager in the quarters and now semis, so I’m guessing if I win they’re going to be, like, finals. It’s just going to keep going. I mean, she’s the greatest player of all time. I’m nothing close to that yet.”

Yet?

Perhaps Gauff actually has higher expectations for herself than the fervent community once known as Tennis Twitter.

After dropping the first set to Sabalenka, Gauff steadied herself. She was, despite what the situation would suggest, the calm -- amid the storm.

Her famously fluky forehand? Sabalenka had 16 more errors from that side. Sabalenka had 16 unforced errors in the deciding set; Gauff had two. Ultimately, it was Gauff’s relentless defense that frustrated Sabalenka, in effect, forcing her into a deal-breaking 46 unforced errors for the match.

This was her fourth three-set victory this fortnight, which underlines her unnatural fortitude. Gauff has now defeated Sabalenka once in each of the past four years -- something no one else has been able to do.

It was nearly midnight on Thursday and Gauff had just completed the last of a series of media obligations outside Arthur Ashe Stadium. A small crowd of well-wishers screamed her name and she graciously stopped for five minutes or so to sign tennis balls and take selfies.

Just as she finished up and started walking back toward the locker room, another group spotted her. There was a brief flicker of irritation in her eyes, but she stopped, stepped outside the protected area and, for a few more minutes, made everyone’s day.

Yes, American tennis is in good hands. Gauff will be ranked No.3 among Hologic WTA Tour players when the new numbers come out on Monday. She might be higher if they factored in humility and honesty.

A year ago, Gauff lost a one-sided Roland Garros final to Iga Swiatek, 6-1, 6-3. Ultimately, she said, that experience was part of her inspiration on Saturday.

“Honestly, the French Open moment,” she said in her post-match interview. “I don’t know if they caught it on camera but I watched Iga lift up that trophy. I watched her the whole time. I said, `I’m not going to take my eyes off her, because I want to feel what that felt like for her.’

“That felt like craziness today lifting this trophy. It hasn’t sunken in and I think it probably will maybe in a week or so.”

Like the 19-year-old she is, sitting in her changeover chair minutes after the match, she was on the phone with her brother Cameron.

“Gotta go, gotta go,” she said, hanging up.

And then they handed her the sterling trophy. It’s way too early to call it a Serena succession, but you get the idea Coco Gauff isn’t going anywhere.

Ten minutes before the match, Gauff said she was scrolling through comments on social media, saying she wasn’t going to win. During the awards ceremony, Gauff made it a point to thank the doubters.

“Thank you for the people who didn’t believe in me,” she said. “A month ago, I won a 500 title -- people said I would stop at that. Two weeks ago, I won a Masters title, and people said that was as big as it was going to get.

“Three weeks later, I’m here with this trophy. To those who thought they were putting water on my fire, they were adding gas to it. Now I’m burning so bright right now.”