GREENBURGH, N.Y. — Mike Sullivan is running into the unavoidable right away, starting his new journey with the New York Rangers against the team, including a handful of players, he will walk together with forever.

“I’m sure there will be a lot of mixed emotions,” Sullivan said.

In a not-so-subtle decision by the NHL schedule makers, opposing the New York Rangers in Sullivan’s debut as their coach at Madison Square Garden on Tuesday is the Pittsburgh Penguins (8 p.m. ET; ESPN, SN1, TVAS), the team he coached for the past decade.

The Rangers also play against the Penguins in Pittsburgh at PPG Paints Arena on Saturday.

“The relationships that I built with those guys were strong,” Sullivan said. “We had the privilege of winning a couple of championships together, and I think when you go through experiences like that it certainly galvanizes relationships that last a lifetime.”

Sullivan arrived in Pittsburgh on Dec. 12, 2015, replacing Mike Johnston, who was fired. The Penguins, with Sidney Crosby, Evgeni Malkin and Kris Letang, were at a crossroads, struggling to get back to the team they were in 2009 when they won the Stanley Cup.

Sullivan got them back to being that team. They won the Stanley Cup in 2016 and again in 2017. They reached the Stanley Cup Playoffs in 2018, 2019, 2020, 2021 and 2022.

The coach parted ways with the Penguins on April 28, a mutual agreement between him and the team, as Pittsburgh’s all-time leader in wins in the regular season (409) and Stanley Cup Playoffs (44).

“Just having him be our coach for that long, that’s pretty rare that a coach has a stint like that,” Crosby said. “Ten years is a long time, and I think the fact that we won together, that we had so much experience with him as our coach — good years where we won and then years where we didn’t make the playoffs — that’s a lot. … I just appreciate all the time that we had.”

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Even with the expectation of an emotional opening night, Sullivan is clear with his next objective.

“What I will tell you is my focus will be on the Rangers and doing our very best to set this group up for success,” Sullivan said.

He began that task on May 2 when he was hired as Rangers coach, replacing Peter Laviolette, who had the job the previous two seasons, leading New York to the Eastern Conference Final in 2024 before missing the playoffs last season.

Sullivan has regularly said before and throughout training camp that his job, and the job of his coaching staff, is to make everyone “a better version of ourselves” every day.

Crosby understands what that means. It’s what he and his teammates attempted to do for 10 years under Sullivan. For the most part, they were successful until missing the playoffs the past three seasons.

Pittsburgh has since decided to go in a new direction, toward getting younger while keeping the three main pieces of the championship core together.

“He meant a lot,” Letang said of Sullivan. “Obviously I’ve tried to learn from every single coach I’ve had, but when you have one that’s been with you for 10 years, it’s something that sticks in your memory, all the little things that you’ve been through, how much time he took with me — not even talking about hockey, more about life in general. I really appreciate that from him.

“But obviously, from the hockey side, he taught me a lot of things I didn’t really see.”

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Sullivan is now trying to change the direction of the Rangers with the same core that went the wrong way last season. It started in training camp, which was, as Crosby predicted, challenging.

“He’s going to push everybody, that’s for sure,” Crosby said before camp began when asked for advice he would give the Rangers players. “He’s somebody who wants to get the best out of you, and to do that, he’s going to push you.”

“Yeah, a hundred percent right,” Rangers forward Will Cuylle said when told of Crosby’s prediction. “I mean, this camp has been tough. A lot of skating. A lot of long days at the rink. To play the style that we want to play we’ve got to be in shape, so I think we’re all pushing each other to make sure we’re in the best shape possible and ready for the first game.”