There are three coaches Amos Jones expects would leave every interview with a job offer.

Bruce Arians. Mike Tomlin. Joe Judge.

That’s esteemed company for Judge, the dark horse who emerged Tuesday from a list of eight candidates as the new head coach of the Giants, pending signing a contract. Almost immediately fans — and even some NFL stars, like Tyrann Mathieu — were Googling, “Who is Joe Judge?” and not finding much.

They would have learned more from Jones, Arians’ special teams coordinator for the Buccaneers. Jones was an assistant coach at Mississippi State when Judge was a senior in 2004, and he urged his reluctant boss, Sylvester Croom, to hire Judge as a graduate assistant the next year.

“I saw a young version of [Steelers coach] Mike Tomlin in him when I first met him,” Jones told The Post. “I took an instant liking to Mike when I met him as a 24-year-old drawing up plays on napkins, and when I got to Joe, I saw that same kind of football intelligence and general want-to-be-great at whatever he is doing.”

Judge was a star quarterback at Lansdale (Pa.) Catholic High School who dreamed of throwing big passes in the SEC. Instead he was a holder, the last line of protection on punts and on the path to special teams knowledge that ultimately put him in the position, as Patriots special-teams coordinator, to be hired by the Giants.

“I put him right in charge of drills where you are coaching players you just played with — some of them you probably drank a beer with at the local establishment,” Jones said. “But Joe never wavered. He was able to handle that without any problem at all. That’s how Coach [Bear] Bryant tested me when I started. That’s how we tested Joe.

“He had no problem with letting them know when they were right or wrong, but he isn’t going to lose his cool just to prove a point. Like Mike Tomlin, he is going to teach you how to be the right kind of player.”

Running his third head coaching search in five years, Giants co-owner John Mara wasn’t committed to an offensive play-caller for rookie quarterback Daniel Jones — Pat Shurmur and Ben McAdoo were too reliant on that ability — or a defensive guru to fix the sullied backbone of the franchise’s tradition.

Mara wanted leadership above all else and found it in the mature-beyond-his-years 38-year-old protégé of Nick Saban and Bill Belichick, arguably the greatest college and NFL coaches of all-time.

“There are certain qualities you have to have being a head coach, and one of them is you have to make decisions that people don’t understand but are your responsibility because you have the HC in front of your name,” said Jackie Sherrill, who recruited and coached Judge at the end of a 38-year career.

“Joey has the temperament to be that person. He has the ability to be a player’s coach, but it doesn’t mean he won’t be a tough guy, like Belichick. He ain’t going to back down. He’s got some of that Jersey/Pennsylvania upbringing.”

Jim Algeo, who coached Lansdale Catholic for 44 years, broke into a wide smile during a rare energetic moment in his hospital bed Tuesday when his daughter shared the news of Judge’s big break.

Just a week ago, as the Patriots prepared for a playoff game and Judge was lining up his first-ever NFL head coach interview with the Giants, he checked in on the man he still refers to as “Coach.”

“He said, ‘I’m praying for your dad, and when the season calms down I’d love to come hang out with him and just talk football,’ ” said John Algeo, Jim’s son. “I sent that message to my siblings who shared it with him, and he got to talking about Joe for a few hours.”

The coach dealt one of his toughest big-shoes-to-fill assignments to Judge: Two-year starting quarterback after the previous two on the job were his son and grandson.

How did it work out? Consider the message on the school’s website Tuesday congratulating Judge within an hour of the news and the random Facebook message John received on Thanksgiving a few years ago.

“Joe said, ‘I was talking to some of the players about how I got into coaching and I realize how much your dad meant to me, what a positive impact he had on me and how a lot of my coaching philosophy is from your dad,’ ” John said. “My dad always talks about how Lansdale is a rare breed. Joe remembering where he came from shows that.”

It reads like a mistake: Special-teams coordinator … and wide receivers coach?

It is not a typo, however. It was a deliberate career move by Judge to broaden his résumé this year — his eighth with the Patriots — in order to raise his profile with his eyes set on becoming a head coach. A decade had passed since John Harbaugh jumped from Eagles special-teams coordinator to Ravens head coach.

“He’s the type of coach who at times seems annoying because of how studious he is,” an NFL veteran who played under Judge told The Post. “He shows you stuff a coach did 10 years ago because he wants to cover every base.

“I remember sitting in his meetings thinking, ‘Do we really need to watch this?’ but you walk away saying, ‘He is doing everything in his power to prepare his guys.’ I think he’ll carry that over to demanding that of the coaches who work under him.”

An opposing NFL coach called Judge “an up-and-coming star.”

“He’s one of the coaches in the building that gets to touch every single player,” the player said. “He has had the chance to coach the 10-year vet and the rookie — in New England everybody does some special teams — and getting all different personalities motivated and ready to play on Sunday.”

As Giants fans are introduced to Judge, his former Mississippi State teammates are angry with their alma mater for letting him get away from their own coaching vacancy. The Giants acted surprisingly fast following Monday’s interview with Judge, fearing losing him after fellow top candidate Matt Rhule received a massive offer from the Panthers.

With three Super Bowl rings and two national championship rings from his time as a special-teams analyst — not an on-field coach — at Alabama, Judge has one for his wife and one for each of their four children.

“You can’t work for Saban and Belichick unless you have managerial and organizational skills,” said Sherrill, who remains in touch with Judge. “Joey always absorbed everything that was being said.”

Jones joked he would “get off a cruise to talk about my son, Joe Judge.” He carries that level of respect among peers and mentors.

Judge’s actual father, a former Temple player, and his mother, an educator, rarely if ever missed a chance to see him in a high school or college game. But it was Jones who accelerated Judge’s career by recommending him for the job at Alabama, where the grooming began.

“He’s one of those guys who’s always had to do the work,” Jones said, “but sometimes didn’t have the title.”

His newest title is a big one.