When the Nets passed over Jacque Vaughn to be their head coach in 2020, he just kept his head down and kept working. When they chased suspended Ime Udoka instead of him earlier this season — over the protests of several female staffers — he stayed focused.

Vaughn — who was named interim head coach on Nov. 1, and had that tag removed a week later — showed the single-minded determination and professionalism that he has demanded from his players, and is instilling in his team. And it’s a big part of why Brooklyn handed him a well-earned contract extension on Tuesday.

Even if it may have been later than it should’ve been.

“I just kept doing my job,” Vaughn said with a shrug on Wednesday. “And it’s a great lesson for my kids. I think at the end of the day, when I talk to them about it — good news, bad news — you just continue to do your job and you persevere and you love to grind, and they know that’s a part of me.

“I’ve seen it all here, whether it’s multiple coaches, it’s the Bubble, whether it’s a toenail over the 3-point line, whether it’s trade requests, whether it’s all of the above. And so to still be a part of this organization means a lot to me. That means the way I carry myself on a daily basis, people appreciate it. So there’s something to that. I just kept doing my job and showing up every single day and ready to rumble every single day.”

After watching him turn Steve Nash’s 2-5 start into a sterling 32-19 record since, the Nets, who held a team option for next season following Vaughn’s early-season promotion, rewarded him with a four-year extension — the length of which was first reported by ESPN’s Adrian Wojnarowski and confirmed by The Post — that will keep him in Brooklyn through 2026-27.

“It’s a huge acknowledgement,” Vaughn said. “Just for the staff, for the comfort of the players, knowing my voice and direction going forward. Being able to really lean into loving this grind and the challenge that’s ahead. Never feared or not walked through those doors before; and so to get rewarded for it is pretty cool.

Vaughn has seen more of this organization than most, in multiple iterations.

A former New Jersey Net for two seasons, Vaughn was the first hire for then-head coach Kenny Atkinson’s staff in 2016-17. He had a pre-existing relationship with GM Sean Marks from San Antonio, and a six-degrees-of-separation-type link with Atkinson, who’d worked under Gregg Popovich disciple Mike Budenholzer.

But none of that got Vaughn the top job in 2020 when Atkinson got the ax. Vaughn went 7-3 as interim — guiding the Nets into the playoffs in the Orlando Bubble — but Brooklyn chose the inexperienced Nash despite having never even been an assistant. Vaughn was kept on as one of the league’s few million-dollar assistants.

When Nash and the Nets parted ways seven games into this season, Vaughn again was named the interim replacement, this time while the organization courted Udoka, largely at Kevin Durant’s behest.

But on a chaotic team beset by constant drama, Vaughn couldn’t control the outside noise any better than Nash did; but he did manage to keep the team focused on basketball, preparing and playing in a professional manner no matter what was going on around them, from injuries to suspensions to other controversies.

“Jacque has made an immediate and immeasurable impact on our entire organization since assuming the role of head coach earlier this season,” Marks said.

“On the court, he’s clearly demonstrated his leadership through his ability to connect and communicate at a very high level while displaying tremendous instincts for the game. As a person, they don’t come any better than Jacque. His character is impeccable, and there is not a better representative for our team and our borough. We are thrilled to have Jacque lead the Nets for years to come.”

Vaughn got that chance — maybe later than he should have — because he got the Nets to play the way he coached.

Make that his Nets.

“I approach my job [simply] every day: I give everything I have, every ounce, and I reload and try and do it again the next day,” Vaughn said. “I knew there was some conversation behind the scenes going on, but for me I didn’t worry about it or get stressed about it or put any additional food on my plate at all. Just did my job every day, and [now I’m] being rewarded for doing that.”

With Durant and Kyrie Irving, the Nets had far more talent than the young, green, barebones Magic teams that Vaughn coached to a 58-158 mark from 2012-15. But he’s also a far more experienced coach now, his seasoning visibly apparent in his salt-and-pepper beard and clean-shaven head.

Now, the Nets he’s coaching coming out of the All-Star break are different from the ones he inherited from Nash, or even the ones he had three weeks ago. Durant has been traded to Phoenix and Irving dealt to Dallas, Brooklyn now bereft of its former MVP and perennial All-Star.

Mikal Bridges — who came from the Suns with Cam Johnson in the seismic Durant trade — will be a focal point of the offense. Along with Dorian Finney-Smith (acquired from the Mavericks), Royce O’Neale and Nic Claxton, he’ll also help anchor the defense, which Vaughn will have to make the club’s bedrock identity to have any hopes of winning.

Assistant Igor Kokoskov has coached Bridges, O’Neale, Finney-Smith and Spencer Dinwiddie in the past, and Vaughn said he’s leaning on the Serb moving forward.

Brooklyn came into the All-Star break at 34-24, sitting fifth in the Eastern Conference. They had a two-game lead on the sixth-seeded Knicks, and 2 ½ on Miami, a cushion padded with their superstars that they’ll now have to hold onto without them.

While Vaughn has clearly matured since his days in Orlando, trying to concoct ways to win sans Durant and Irving may see him grow again. At least so says Erik Spoelstra, coach of those aforementioned Heat.

“It’s a fruitful coaching experience,” Spoelstra said. “In this league, you get better trying to find a solution with expectations that don’t change when the reality does change a little bit. I know when we went through that, we got a lot better as a coaching staff.”

That was in 2014-15, after LeBron James had left Miami to return home to Cleveland. It broke up the so-called Heatles of James, Dwayne Wade and Chris Bosh, and saw 37-45 Miami miss the playoffs the following season.

The Heat have made the postseason in five of the next seven, including a 2020 Finals berth. Vaughn doesn’t have Spoelstra’s resume or his roster (there is no Wade or Bosh in Brooklyn), but he does have a willingness to work and an eagerness to improve. He’s imparted both on his team.

“I just think I learned as a coach along the way. The relationship — more than what play I’m going to run for a guy — will continue to be able to withstand wins, losses, all of the above. So I probably focus my mind on it that way, how I communicate with a guy, when to communicate with him, what he needs. Probably didn’t look at it that way as a young coach.”

So far, that mindset has these new-look Nets still in the thick of the playoff race, even if their future is uncertain.

That’ll have to be a start.

The Nets are averaging 68,000 viewers per game on YES, the third-best All-Star Break numbers since moving to Brooklyn. Even  more encouraging is the fact they haven’t cratered since the Durant trade.

In the three tilts on YES since the Durant trade (discounting Friday), they averaged 92,000 total viewers. That was up 37 percent from the 67,000 average pre-trade.

Cam Thomas has filed for a trademark on ‘Ain’t Sh-t Funny,’ according to NetsDaily.