Last Sunday, Gerrit Cole became an All-Star for the sixth time in his 11-year career.

But he has only actually pitched in the game once.

Could his second appearance come Tuesday with him starting the game for the first time? The Yankees ace has a shot.

“One of these days, I would really like to start it,” Cole said after being named an All-Star. “I gotta check that one off. But I’m not sure how that shakes out over the next week.”

Cole is scheduled to start Saturday’s game against the Cubs for the Yankees, which would then put him on two days’ rest for the Midsummer Classic.

That’s not ideal, but if Cole treats it like a between-starts bullpen session, it could make sense.

In his only All-Star Game appearance, in 2015, he pitched on three days’ rest. The other four times he was voted in as an All-Star, he would have been pitching on one or two days’ rest.

There is also the fact that the Yankees don’t currently plan on Cole starting the first game out of the All-Star break. They are hoping to have Carlos Rodon make that start next Friday against the Rockies. Domingo German would be on an extra day’s rest to start on Saturday, before the Yankees could slot Cole in on Sunday, which would be five days after his potential All-Star appearance.

One other factor helping Cole is the attrition from other starting candidates. Rays ace Shane McClanahan, up until recently viewed as the favorite to start, landed on the 15-day IL on July 1 with mid-back tightness. Angels two-way star Shohei Ohtani also exited his start on Tuesday with a blister, after which he revealed that he does not plan on pitching in the All-Star Game.

Before that, Cole had mentioned Ohtani and Nathan Eovaldi as two of the more deserving candidates to start the game.

“Hey, you know what?” he said. “If I don’t like it, I gotta pitch a little better, I guess. That’s the key.”

Here’s who could stand in Cole’s way of starting his first All-Star Game:

Nathan Eovaldi

The former Yankees (and Red Sox, Dodgers, Marlins and Rays) right-hander figured to play second fiddle to Jacob deGrom on the Rangers, but instead Eovaldi has been both healthy and terrific. After a somewhat shaky start Thursday in Boston, he’s 10-3 with a 2.83 ERA and 109 strikeouts in 117 ⅔ innings. This will be only the second career All-Star Game for the 33-year-old, but he is probably Cole’s stiffest competition to start it. Aiding his case is that he started Thursday, putting him on full rest for Tuesday, and that the Rangers have been one of the surprises of the first half, leading the AL West.

Framber Valdez

The Astros ace, who like Cole is scheduled to start on Saturday, certainly warrants consideration. He is 7-6 with a 2.49 ERA — which is best among qualified starters in the American League — and 110 strikeouts in 105 innings. But the second-time All-Star also might have a slight edge over the rest of the field because it will be his own manager, Dusty Baker, who will make the decision on who starts the game.

Sonny Gray

This will be Gray’s third trip to the All-Star Game, one for each of the teams he has been on not named the Yankees. The Twins right-hander, another scheduled Saturday starter, is 4-2 with a 2.50 ERA and 96 strikeouts in 93 ⅔ innings. He allowed just three runs in 35 innings in April, and has not given up more than three runs in any single start this season.

Kevin Gausman

The Blue Jays ace has been the most valuable starting pitcher in either league so far this season, at least according to FanGraphs’ version of WAR, which has him at 3.8 — with Valdez the next-closest (3.0) in the AL. The 32-year-old right-hander, making his second All-Star team, is 7-4 with a 3.04 ERA and an AL-best 146 strikeouts in 109 ⅔ innings. He is also scheduled to start on Saturday.

Luis Castillo

This would be the sentimental hometown pick, starting the Mariners ace at his home park. Castillo, who will start on Friday, enters that outing 5-6 with a 3.05 ERA and 114 strikeouts in 100 ⅓ innings. It will be his third All-Star appearance, this one in front of an adoring crowd in Seattle.

Cole, meanwhile, is in the midst of his best season as a Yankee. He enters Saturday’s start 8-2 with a 2.79 ERA and 118 strikeouts in 109 ⅔ innings. Anchoring a rotation that has been besieged by injuries and inconsistency, Cole has taken the ball every five (or six) days and delivered the Yankees what they expected when they signed him to a nine-year, $324 million contract ahead of the 2020 season.

This spring, Cole made it known how much more comfortable and settled he was feeling entering his fourth season as a Yankee, and it has shown in his performance.

After home runs hurt him last season, he has done well to limit them this year, giving up only 10 — eight of them coming in a five-start stretch in May.

Part of a rotation that has had too many short starts, Cole has delivered six or more innings in 13 of his 18 starts.

“It’s impressive,” said Aaron Judge, who at the moment is the Yankees’ only other All-Star, though he won’t play in the game. “That’s what this guy does day in and day out, year after year. He continues to produce. He posts every year, 30-plus starts.

“I saw him from afar for so many years. Getting a chance these past couple of years to watch him up close, how he prepares, how he works, how he helps his teammates out, even when other guys are starting … he’s always helping them out in-game. Seeing him not only be a great teammate but also show up and produce every five days, it’s exciting. I’m happy for him.”

Want to catch a game? The Yankees schedule with links to buy tickets can be found here.

At long last, Carlos Rodon’s Yankees debut is here.

Nearly seven months after he signed a six-year, $162 million contract, Rodon will throw his first pitches for the Yankees on Friday night in The Bronx against the Cubs.

A forearm muscle strain after one spring training start derailed Rodon’s hopes of being ready for Opening Day, and back discomfort slowed his recovery.

Throughout his whole rehab process, though, Rodon has shared in the fans’ frustration that he has not been available. Now it will be up to him to deliver the results, with the pressure turned up even more after he missed the first three months of the season.

In a coincidence, Rodon will square off against Jameson Taillon, the pitcher he essentially replaced in the Yankees rotation. The Cubs gave Taillon a four-year, $68 million contract, but it has been a rough go for the right-hander after leaving the Yankees. He enters with a 6.93 ERA in 14 starts, and missed two-plus weeks in April with a groin strain.

It’s possible the Yankees could have another player added to the All-Star roster as an injury replacement at some point this weekend.

Clay Holmes would be the top candidate. Aaron Boone also campaigned for Gleyber Torres to make it.

But if that does not happen, the Yankees’ two All-Stars (Judge and Cole) would be their fewest since 2013, when Robinson Cano and Mariano Rivera made it. The previous time it happened was 1993 (Wade Boggs and Jimmy Key), which came after a three-year run in which they only had one All-Star each season (1992: Roberto Kelly; 1991: Scott Sanderson; 1990: Steve Sax).

The last time no Yankee appeared in an All-Star Game was 1991.

One other Yankees-related thing to watch during the All-Star festivities? Outfielder Spencer Jones and right-hander Clayton Beeter are set to play in the Futures Game on Saturday.

Jones, the 22-year-old who garnered comparisons as a left-handed hitting Aaron Judge when he was drafted last summer, is batting .263 with a .800 OPS, 10 home runs, 21 steals and 98 strikeouts in 68 games with High-A Hudson Valley.

Beeter, the 24-year-old whom the Yankees acquired from the Dodgers for Joey Gallo last summer, has a 2.64 ERA and 83 strikeouts across 14 starts this season — 12 at Double-A Somerset before making the past two with Triple-A Scranton/Wilkes-Barre.

It was just last year the Yankees’ Futures Games representatives were Anthony Volpe, Jasson Dominguez and Ken Waldichuk. It serves as a good reminder that playing in the game does not guarantee a straight arrow to The Bronx.

Volpe has been inconsistent with the Yankees (though he has looked much better over the past three weeks), Dominguez is scuffling at Double-A and Waldichuk is with the A’s after being packaged in the Frankie Montas trade two weeks after last year’s Futures Game.