SAN FRANCISCO — Just hours before Mike Dunleavy Jr. was set to take center stage for his introductory news conference as the Warriors’ new general manager, word broke that Draymond Green was planning to opt out of his player option, which would make him an unrestricted free agent.

Consider this to be the first big domino to fall on Dunleavy’s watch. What he does next will dictate the Warriors’ direction.

So much for getting to bask in the glow of the new job. Dunleavy is being thrown into the fire in the midst of a pivotal offseason for the title-hungry Warriors.

Negotiating with Green, who was set to make $27.6 million next season, is one of several key topics for Dunleavy and the Golden State front office in the coming days, along with Thursday’s NBA Draft and free agency opening July 1, as well as a potential extension for Klay Thompson.

The 42-year-old executive couldn’t directly discuss Green’s imminent decision Monday due to league rules, but he reiterated what Steve Kerr and others had said since the season ended.

“We really want Draymond back,” Dunleavy said. “What he means in terms of this organization and this team, winning at the highest level, we feel like we have to have him. So that’s very important.”

Green, 33, doesn’t have to officially opt out until the June 29 deadline, but his agent Rich Paul told ESPN’s Adrian Wojnarowski that they plan to “explore all options,” including remaining with Golden State.

Beyond keeping the Warriors’ veteran core intact, Dunleavy said he’d like to add more shooting and connectivity, as in ball-handling, passing and experience, in order to make the Warriors a more formidable threat.

That all sounds nice, but it’s easier said than done, especially given the Warriors’ sticky financial situation. Golden State’s combined salary and luxury tax penalties have ballooned over $450 million, and the NBA’s new collective-bargaining agreement is dropping the hammer on high-spending teams, taking away roster restructuring measures such as the mid-level exemption.

Still, Dunleavy remains optimistic that he can identify players in the draft and free agency to plug holes around the team’s dynastic trio.

“A lot can be made of all the challenges that are coming our way, whether it be [the] aging roster, the new CBA with some of the limitations there, anything else you can bring up,” Dunleavy said. “We’re aware of all those things, but we also feel like we’re in a great place because we’ve got a competitive owner willing to spend, a group that’s tied in, has good synergy, good processes, good, sound decision making. We feel confident we can navigate it.”

Warriors owner Joe Lacob tapped Dunleavy to be Myers’ successor because he saw the former player as a “spectacular” culture fit after five years in the front office.

“He’s a very collaborative person, which is very, very important,” said Lacob, who didn’t interview any candidates outside the Warriors’ organization. “I’ve said it a million times in our organization, it’s a ‘we’ thing. I can’t emphasize how important that is… Mike fits right into that.”

Dunleavy’s comfort and trust with the Warriors should help him with the coming difficult conversations with some of the team’s key players, including Green.

Dunleavy, whom Bob Myers had been grooming for this moment, said he’s developed good relationships with the organization’s core people and reached out to many of them over the last week after being promoted from vice president of basketball operations.

“We have the mutual respect of having played,” said Dunleavy, who played 15 years in the NBA after being drafted No. 3 overall by the Warriors in 2002. “(I’m) nowhere as accomplished as those guys, but I think there’s a mutual bond and understanding.”

Dunleavy has been discussing his vision for the team with the coaching staff and players for weeks now, and he said he has a good idea of what needs to be done.

“Fortunately, it’s nothing drastic,” he said. “But there’s things we can do around the margins, make a move here or there. We’re going to be open to it.”

Failing to make it out of the second round of the playoffs was a disappointing end to a disjointed season for the Warriors, who had not lost a playoff series to a Western Conference foe since before Steve Kerr arrived in 2014.

Kerr partially blamed the season’s shortcomings on fractured team culture and a lack of connectivity. He said last month that rebuilding that championship identity is an offseason priority.

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Dunleavy agrees.

“The core group of guys, led by Steph Curry, is at an incredibly high level,” Dunleavy said. “For that reason, we feel we have a chance to always be knocking on the door. The rest of the roster going on down the line is a group that probably needs to be better about playing together and connecting, so that’s something we’ll look to solve for this offseason.”

When Dunleavy watched the Denver Nuggets win the NBA Finals last week, he saw a team “dialed in together” like the Warriors were in 2022 and said he believes Golden State can find that level again.

Next up for Dunleavy is the draft, an opportunity to add a player with the No. 19 pick, or potentially make a trade. He brushed off trade rumors involving Jonathan Kuminga and Jordan Poole, though he didn’t say whether any players — beyond the obvious, Curry — would be untouchable.

“Frankly, we get a lot of calls,” Dunleavy said. “People value guys on our roster. I think we’re in good shape in that respect.”