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NEW YORK — For 20 minutes, the chances that an American could actually win the U.S. Open for the first time in 21 years looked very good, or at least as good as they had been in a long time.

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

And on Monday night, Tommy Paul thrashed world No. 1 Jannik Sinner to take a 4-1 lead in the first set by breaking the Italian’s serve twice in his first three attempts.

Sinner was throwing forehands and backhands all over the park. Paul was doing what he felt the ball and his game: he was jumping back to the service line between points, spinning his racket, hitting the court and releasing the ball.

Inside the packed Arthur Ashe Stadium, which was lit up at night, the noise grew louder. Chants of “USA” echoed through the building.

Did this really happen?

Tommy Paul felt 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 present, including Tiafoe and Fritz – who were no doubt watching their long-time friend fight for the win from their hotel rooms – how difficult it would be to win this tournament. Suddenly he was hitting his forehands inches over the net and millimeters from the line, his long legs propelling him back and forth across the baseline, changing direction like a slalom skier cutting through the gates, something he used to do as a kid.

Now Paul was moving backwards instead of forwards, throwing balls around. The trophy that Andy Roddick lifted in 2003, when it still looked like the American men won this thing every two years or so, was receding further and further away.

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

“I’m playing against the number 1 in the world 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.

“Different parts of the drawers opened, but mine didn’t.” No, it didn’t.

Paul had spent the first part of the match avoiding what he calls “bang-bang tennis,” the baseline rallies where Sinner hits the ball harder than anyone else. He scurried unseen into the net. He developed clever patterns, hitting cross-court forehands down the line to Sinner’s backhand before scurrying to the opposite corner to receive the next ball.

From there, he hit a short slice into the Italian’s forehand, the ball stopping on the service line. Anything to stop Sinner from unleashing a thunderbolt that could even pierce the rumble of Arthur Ashe Stadium. He held off fate for two sets.

Then Paul was leading 4-3 in the second set tiebreak and came to the net. Sinner hammered a passing shot straight at him. A volley into the corner and it was 5-3 for Paul, but the ball was just too fast. He stopped it in midcourt. Sinner went past him and that was basically the end. 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 see through Sinner themselves.

There is still a long way to go, as Tiafoe warned after beating Alexi Popyrin on his favorite court in front of fans who got incredibly loud for him.

“You can’t go overboard,” Tiafoe said. “Everyone is good, so it doesn’t really matter who’s there and who’s not.”

Tiafoe will face Grigor Dimitrov on Tuesday night at Ashe Stadium. Maybe he and his 24,000 friends will throw another party in the stands. Or maybe Dimitrov’s nasty slice backhand will rip his forehand to shreds, like it did at Wimbledon last year, when Tiafoe was still riding the confidence of his semifinal run at that tournament in 2022.

This was their first meeting in four years. The head-to-head ended 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 foray from Andrey Rublev on Sunday. He also had his best season in years under the tutelage of Jamie Delgado, an old-school coach who demands hard work and hard tennis from a player who for years showed little interest in either.

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

Could it possibly be Fritz, which would give the Americans a guaranteed place in the final?

Perhaps.

Fritz beat Zverev at Wimbledon, fighting back from a two-set deficit. Zverev, this year’s defeated French Open finalist, said he was playing on one leg. Not very generous. He was limping, having hyperextended his knee in an earlier round, but he and Fritz have traded victories since 2018. It seems it’s Zverev’s turn now, although he hasn’t been as good as he was during the clay-court season. Whoever serves better will likely win.

Like Tiafoe, Fritz is trying with 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 it. Djokovic, whom he has never beaten, was absent from 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 forward again.

Think about the person standing in front of him and go from there.

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

“I think as you get better, expectations go up,” he said.

“In the past, I was always very happy when I reached the quarterfinals. Now I’m still happy when I reach the quarterfinals, but I wouldn’t be happy if it ended here.”

If he beats Zverev and then has to face Dimitrov, he will remember his victory in Rome this spring. However, that was on clay, in best-of-three format, not best-of-five.

If Fritz or Tiafoe make it to 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 take him out of the match.

Medvedev is the 2021 champion. But Fritz might prefer it otherwise. He has beaten Sinner once, and his record against Medvedev is 0-1.

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

There is still quite a long way to go to get this trophy.

(Top photo: Sarah Stier / Getty Images)