NEW YORK -- The Yankees say they have not decided how they’ll adjust the rotation once Gerrit Cole is ready to reclaim his ace slot. Perhaps so, but this much is certain: Whatever their formula between now and October, Luis Gil deserves to be a part of it.

Gil continued to make the most of his unexpected chance in the starting five, permitting just an infield hit across 6 1/3 innings in the Yankees’ 5-0 victory over the Mariners on Thursday afternoon at Yankee Stadium.

“It’s being focused on what I need to do out there, going out and executing a plan of attack,” Gil said through an interpreter. “You look at this team and the support they’ve given me all year round; a combination of many different things have led me to this.”

Three relievers combined to finish the shutout in relief of Gil, who improved to 5-0 with an 0.59 ERA in five May starts. As he exited in the seventh, Gil received a standing ovation from the crowd of 43,121, beaming as he raised his cap high.

Brought back from Minor League camp following Cole’s right elbow injury this spring, Gil has parlayed a dazzling spring into a contending bid for the American League Rookie of the Year Award.

“When you’ve got a guy [like Cole] that just won the Cy Young go down, that’s going to impact the staff and impact the team,” said captain Aaron Judge. “And it has. But to get a chance to see Gil consistently go out there and show us what he showed before he got hurt [in 2022], it’s been a treat.”

Thursday’s effort improved Gil’s season record to 6-1 with a 2.11 ERA in 10 starts. There have been only three Yankees to fire at least six innings while allowing one or zero runs over five consecutive starts, with Gil joining Steve Kline (1972) and CC Sabathia (2011).

“He just continues to get better and better,” manager Aaron Boone said. “He’s got so many weapons that can beat you.”

Gil points to his frequent chats with Cole and pitching coach Matt Blake as something that has helped his development, with Gil saying that his focus during those sessions has been “to listen and to execute.”

“What they’ve provided has been great for me,” Gil said. “It’s really understanding how things are going to help me out there in-game. For example, making sure that my mechanics are the same, compact and consistent.”

Said Boone: “I think he’s developed a really good routine. And then his work has been excellent, not just between the lines but on the other days. He’s learning, growing, and it’s been fun to watch.”

As the Yankees jet to the West Coast this weekend, Cole is bound for Tampa, Fla., where he’ll continue sessions against live hitters. Minor League rehab games will follow, and soon the Yankees could have Cole back where he belongs.

What will that mean for Gil and the rest of the rotation? Boone said he hasn’t plotted it out yet.

“It’s three, four, five, six weeks away,” he said. “If, at that point, we’re in this position, then that’s a good thing. We’ll do what we have to do, what we think is best for the team and everyone involved. In the baseball calendar, that’s still light years away.”

Giancarlo Stanton and Judge hit early homers off Seattle starter Luis Castillo, with Stanton launching his 12th and Judge slugging his team-leading 15th. New York pulled away with three runs in the seventh, securing a split of the four-game set.

One outing after setting a franchise rookie record with 14 strikeouts against the White Sox on May 18, Gil retired the first nine batters he faced. J.P. Crawford broke that string by reaching on a grounder that shortstop Anthony Volpe bobbled but was scored a hit.

Had an error been charged, it would not have altered the Yankees’ handling of Gil, who exited after his 96 pitches (65 strikes).

Though Boone said there are no set limitations for Gil, such as the arbitrary numbers that irked rookie phenom Joba Chamberlain a decade and a half ago, the Yankees cannot look past the fact that his innings total is rising.

Gil has now thrown 55 1/3 frames; in 2021, when he advanced from Double-A to Triple-A and then the Majors, Gil tallied 108 2/3, a pace he’s ahead of now. The Yankees also must consider that while Gil says he feels “pretty good,” Tommy John surgery is not far in his rearview mirror.

“We’ll pay attention to everything,” Boone said. “If that time comes to where it’s starting to show and an innings limit happens, then so be it. But there’s no limit we’re putting on things. As we go, we may dial it back in a certain outing, but it’s full steam ahead.”