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NEW YORK — For 20 minutes, the chances of an American man winning the US Open for the first time in 21 years seemed very good, or at least better than they had in a long time.

Carlos Alcaraz left the tournament on Thursday night. Novak Djokovic followed him out the door on Friday. Taylor Fritz and Frances Tiafoe, who were playing their home Slam, were already in the last eight.

And on Monday night, Tommy Paul gave world number 1 Jannik Sinner a good beating, taking a 4-1 lead in the first set by breaking the Italian’s serve twice in his first three attempts.

Sinner was flying forehands and backhands all over the park. Paul was doing that thing where he felt the ball and his game: jumping back to the service line between points, spinning his racket, pushing up the court and going for the ball.

The packed Arthur Ashe Stadium, glowing in the night, grew louder. Chants of “USA” filled the building.

Did this really happen?

Tommy Paul felt right at home on Arthur Ashe… until Jannik Sinner reminded him how hard it is to win a Grand Slam. (Angela Weiss/AFP via Getty Images)

That was it, for 20 minutes. After 25 minutes, Sinner showed everyone here, including Tiafoe and Fritz — who were no doubt watching their old friend fight the good fight from their hotel rooms — how hard it would be to win this tournament. Suddenly, Sinner was driving his forehands inches over the net and millimeters off the line, his long legs pushing him back and forth along the baseline, changing direction like a slalom skier cutting through the fences, which is what he used to do as a kid.

Now Paul was going backwards instead of forwards, spraying balls everywhere. The trophy that Andy Roddick held aloft in 2003 — when it seemed like American men were destined to win this thing every year or so — was fading further and further into the background.

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None of this surprised Paul. He had heard the chatter after Djokovic and Alcaraz had left. Big chance. No better chance. The draw was wide open for the three Americans who had spent all those nights as teenagers in USTA camps in Florida and California.

“I’m playing against the world number 1 tomorrow, “So I don’t know if I think too much about chances,” he said Saturday after his third-round win over Canadian qualifier Gabriel Diallo.

“Several parts of the draws have opened, but mine hasn’t.”

No, that was not the case.

Paul had spent the early part of the match avoiding what he calls “bang bang tennis,” the baseline exchanges where Sinner cracks the ball harder than anyone else. He crept into the net unseen. He developed clever patterns, taking cross-court forehands down the line to Sinner’s backhand, before racing to the other corner to receive the next ball.

From there he cut short into the Italian’s forehand, the ball dying on the service line. All to prevent Sinner from unleashing a thunderclap that even pierced the rumbling of Arthur Ashe Stadium. For two sets, it blocked fate.

Then Paul was up 4-3 in the second-set tiebreak, and he came to the net. Sinner hit a passing shot straight at him. A volley into the corner and it was 5-3 Paul — but the ball was just too fast. He stopped it in the middle of the court. Sinner passed him, and that was basically that. The Italian went through, 7-6(3), 7-6(5), 6-1.

If Fritz or Tiafoe want to win the US Open, they will probably have to deal with Sinner themselves.

That’s still a long way off, Tiafoe warned after beating Alexei Popyrin on his favorite court, in front of fans who played ridiculously hard for him.

“You can’t get ahead of yourself,” Tiafoe said. “Everyone is good, so it doesn’t really matter who’s in or out.”

Tiafoe will face Grigor Dimitrov on Tuesday night in Ashe. Maybe he and his 24,000 friends will throw a party in the stands. Or maybe Dimitrov’s nasty slice backhand will shred his forehand, as happened at Wimbledon last year when Tiafoe was still enjoying the confidence he had for his semifinals at this tournament in 2022.

That was their first meeting in four years. The head-to-head is 3-1 for Dimitrov, and Tiafoe last defeated him in 2019, at the Australian Open. It lasted four sets and the score was 7 in all four sets.

Frances Tiafoe loves Arthur Ashe Stadium like no other. (Angela Weiss / AFP via Getty Images)

That was a tennis lifetime ago. Dimitrov is 33 and survived a two-set run from Andrey Rublev on Sunday. He’s also had his best season in years under Jamie Delgado, an old-school coach who coaxes hard work and tennis out of a player who has shown little taste for either for years.

After a year in the wilderness, Tiafoe wins the only way he knows how: with heart and soul. He wins points with bursts of power and gentle touch, and he rides the crowd like a preacher rousing his congregation on a Sunday morning. If he can get past Dimitrov, he will play the winner of Fritz and Alexander Zverev, the No. 4 seed.

Could it be Fritz who gives the Americans a guaranteed spot in the final?

Maybe.

Fritz defeated Zverev at Wimbledon, coming back from a two-set deficit. Zverev, this year’s defeated French Open finalist, said he was playing on one leg. Not very magnanimous. He was handicapped, having overextended his knee in an earlier round, but he and Fritz have been trading victories since 2018. It looks like Zverev is next, although he is not as sharp as he was during the clay court season. Whoever serves best will probably win.

Like Tiafoe, Fritz uses every fiber of his brain not to think about a path to the final. He showed up at the 2022 US Open thinking he had a chance to win. Djokovic, whom he has never beaten, was not at that tournament because he refused to be vaccinated against the coronavirus.

Fritz lost in the first round to a qualifier named Brandon Holt. Since then, he has vowed never to look ahead again. Worry about the person sitting across from you and look at it from that perspective.

Taylor Fritz played a tough match against Casper Ruud and reached the quarterfinals. (Angela Weiss / AFP via Getty Images)

“I think as you get better, your expectations increase,” he said. “I used to be very happy to get to the quarter-finals. Now I’m still happy to get to the quarter-finals, but I wouldn’t be happy if it ended here.”

If he gets past Zverev and then faces Dimitrov, he will have the memory of beating him in Rome this spring. But that was on clay, in a best-of-three instead of a best-of-five.

If Fritz and Tiafoe make it through Sunday, they’ll likely see the world No. 1 on the other side of the net — unless Sinner loses on Wednesday. He’ll play Daniil Medvedev, the player most likely to knock him out.

Medvedev is the 2021 champion. But Fritz might prefer it the other way around. He has already beaten Sinner once, compared to a 0-1 record against Medvedev.

Tiafoe? Winless in five games against Mevedev, and 1-4 against Sinner.

That trophy is still a long way off.

(Top photo: Sarah Stier/Getty Images)