MIAMI GARDENS, Fla. — In a decade or so, after Carlos Alcaraz has piled up the Grand Slam tournament trophies, a four-week stretch in early 2022 may stand out as the time he took over tennis.

Over the last month, in tennis’ annual first-quarter pilgrimage to the United States, Alcaraz, 18, of Spain, ceased to be an up-and-comer.

At the two most significant American tennis tournaments other than the U.S. Open, the BNP Paribas Open in Indian Wells, Calif., and the Miami Open, he made clear that he is not the future; he is the now. With each round this weekend in Florida, the gasps at his cracking forehands and the chants of “Vamonos” and “Let’s go, Carlos” echoed more loudly at a stadium displaying plenty of Spanish flags.

On Sunday, Alcaraz overcame early jitters to beat Casper Ruud of Norway, 7-5, 6-4, and captured his first Masters 1000 tournament title — the level just below the Grand Slam events.

Ruud, known until lately as a clay-court specialist, came out slugging, breaking Alcaraz’s serve in the first game of the match. But with each game, Alcaraz seemed more comfortable and applied more pressure, especially when Ruud was serving. Ultimately, Ruud, 23, fell to a player who was more athletic, more creative and more talented, and who is somehow able to grind with anyone, even as a teenager.

“You’re such a good player already,” Ruud told his opponent when it was over.

Alcaraz collapsed onto his back when a final slicing volley sealed the victory. He grabbed his head in disbelief, though he might have been the only doubter in the stadium. Soon, he was embracing his coach, Juan Carlos Ferrero, and his father, also named Carlos.

Ferrero, who calls himself Alcaraz’s “invisible whip,” was in tears. He arrived Saturday, after his father died. But he and Alcaraz’s father wanted to be here to witness the culmination of a staggering month. Their prodigy had tantalized tennis fans on the West Coast, where he tore apart seasoned veterans like Gaël Monfils of France and Roberto Bautista Agut of Spain. In the semifinals, he nearly toppled the player he is compared to most often, Rafael Nadal, the 21-time Grand Slam tournament champion who is also from Spain. He then ran the table in Florida.

“I am not afraid to say I want to win a Grand Slam,” said Alcaraz, who said he received a congratulatory call from King Felipe VI of Spain after the win. “I know it is going to be really hard, but I am not afraid to say it.”

No one would dare predict that there are not many more trophies in Alcaraz’s future. In Indian Wells, Nadal could barely pay attention during a news conference as Alcaraz’s match played on a television behind him and he anticipated an approaching showdown. Someone pointed out that Alcaraz was down an early service break to the reigning champion, Cameron Norrie of Britain.

Nadal smiled. “Many games remain,” he said. Alcaraz won in straight sets.

Now, depending how he does at the clay-court tournaments in Europe ahead of the French Open, Alcaraz could arrive at Roland Garros as a favorite.

The rise of Alcaraz has been on the horizon for years. There was buzz that another version of Nadal was evolving under the guidance of Ferrero, a former No. 1-ranked singles player, at his academy in Alicante, Spain. Alcaraz made his debut in a Grand Slam event at 17 at the 2021 Australian Open, where he won his first match. He had yet to crack the top 100 when he played here last year. By September, he was a U.S. Open quarterfinalist.

But this era, however brief it was going to be, was supposed to belong to the so-called Next Gen threesome of Daniil Medvedev of Russia, Alexander Zverev of Germany and Stefanos Tsitsipas of Greece, all in their early or mid-20s and primed to claim the sport from the aging Big Three of Nadal, Roger Federer and Novak Djokovic.

Other than Medvedev’s triumph at the 2021 U.S. Open, that group is still looking for the most important championships. With Djokovic prohibited from playing most tournaments after his refusal to be vaccinated against Covid-19, Medvedev captured the No. 1 ranking in late February, but lost it after an early loss at Indian Wells. Medvedev, Zverev and Tsitsipas have won zero titles through the first quarter of the year.

As the tour moves to Europe’s red clay, Medvedev’s worst surface and possibly Alcaraz’s strongest, Medvedev is in danger of becoming an answer to a trivia question about players who held the top ranking for the briefest periods. Alcaraz’s skill and power may be too much to hold off for much longer.

Oddly, as hard as Alcaraz hits the ball — so hard that Tsitsipas said last September that it took him a full set to get used to his pace — his most devastating play may be his drop shot. Just as Ruud — or Monfils, Bautista Agut or any opponent — was dug in and battling, there came yet another drop shot, falling like a feather.

“It’s crazy how good he plays,” said the 6-foot-5 Hubert Hurkacz, a 25-year-old from Poland who was the reigning champion at the Miami Open.

This was about an hour after Alcaraz had outdueled Hurkacz in two tiebreakers in their semifinal Friday night. “Incredible, how he plays, how he competes,” Hurkacz said.

The win over Hurkacz came 24 hours after Alcaraz had outlasted Miomir Kecmanovic of Serbia, despite losing the first set and being down by 5-3 in a tiebreaker, this one in the third set. Alcaraz stormed back and sealed the match by pushing one last winner down the line. Kecmanovic, a sweat-soaked mess after being run ragged for nearly two and half hours, gazed upward as though Alcaraz had just swindled him out of his per diem.

Alcaraz is developing a reputation for wearing down opponents. Midway through the second set on Sunday, the ending seeming inevitable, a tiring and cramping Ruud had to call for a trainer, and spent several minutes being stretched out.

Ferrero said the victory would help Alcaraz grow not just as a tennis player but also as a person.

“I think it is going to happen many times,” said Ferrero, who added that Alcaraz was not even at the halfway point of his development. “He is growing up so fast.”

Now, he said, comes a day or two of golf, of relaxation, and then more work. And then, more likely than not, more trophies.