The Yankees' Aaron Judge flips his helmet after taking batting...

The Yankees' Aaron Judge flips his helmet after taking batting practice with live pitching at Yankee Stadium before an MLB game against the Royals on Sunday. Credit: Kathleen Malone-Van Dyke

After a week-plus of Aaron Judge taking full batting practice and running the bases, the Yankees determined the outfielder was ready for his next significant step in his rehab from the sprained right big toe that has kept him out since June 4.

Judge played in a simulated game Tuesday in Tampa at the club’s minor-league complex, a controlled environment with Yankees’ minor leaguers in which he played roughly five innings.

“Hit a long home run to right-center in one of his ABs and appeared to be moving around well,” said one talent evaluator who was in attendance. “I did not see him favoring [the toe] . . .  I would be encouraged.”

Before Tuesday night’s game against the Mets, Aaron Boone said Judge will play another sim game on Wednesday — which will include, as it did Tuesday, the Yankees’ captain playing in rightfield and running the bases. Everything thereafter will be “day-to-day.”

Which pretty much summarized the manager’s answer when asked if he saw Judge returning in time for this weekend’s series in Baltimore.

“I wouldn’t rule anything out,” Boone said. “We’re day-to-day right now.”

Judge has said from the time he was diagnosed with the injury that the biggest test for him would be running at full speed and being able to stop and start on the toe with a minimal amount of discomfort.

“We’ll try and set up situations to make sure there’s action in play, or script some things a little bit more so that not only is he getting the volume of being out there for an hour or two hours, getting the live at-bats, but trying to replicate things that would come up in the game as much as we can,” Boone said.

Judge, who faced Jonathan Loaisiga in a live batting practice session Sunday at the Stadium, said early last week that his return won’t be predicated on him no longer feeling pain or discomfort in the toe because that simply isn’t realistic. At least, not for the rest of 2023.

“It’s not going to be pain-free,” Judge said. “We’ll just get as close to manageable as we can.”

It is typical for any player missing as much time as Judge has to be sent out on a rehab assignment before returning, but Boone said that won’t necessarily be the case with Judge.

In other words, Judge could be activated after a yet-to-be-determined number of sim games in Tampa.

“Everything’s in play,” Boone said. “We’ll see how it goes tomorrow and I think we’re leaving everything on the table.”

Notes & quotes: Andy Pettitte, hired over the weekend as an organizational adviser, threw out the ceremonial first pitch Tuesday. “Andy’s just so good in the room [clubhouse] and has relationships already with a lot of these guys,” Boone said. Gerrit Cole, who grew up a Yankees fan, is just one example. “You just see the impact he has on, not only pitchers, but all players. It’s Andy Pettitte. He walks in with a lot credibility and credentials. But also with the humility that he’s just easy to approach. The staff loves him, the players love him.” Before throwing the ceremonial pitch — he threw a strike from the mound — Pettitte, who spent 18 years in the majors, including 15 with the Yankees, said of the player reception so far: “It seems they’re excited that I’m around. I’ve had a lot of guys asking me a lot of questions. I think since I’ve been through it and I’ve been through it right here [in New York] and been in their shoes. That’s been a good thing.” . . .  Boone said Nestor Cortes, out since June 5 with a left rotator cuff strain, came through his first rehab outing Sunday with Double-A Somerset OK and will next pitch in a rehab game Friday at an affiliate to be determined. Boone said Cortes will need at least two more rehab outings before the organization would consider activating him

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