For years, New York Giants fans have dreamed that Bill Belichick would grow weary of collecting Super Bowl trophies in New England and, with the end of the Patriots’ dynastic run in sight, return to coach the team for which he once was Bill Parcells’s defensive coordinator. It has always been just that — a dream — and it remained so Tuesday.

But when the Giants made their stunning pick to succeed the fired Pat Shurmur as their coach, it was a Belichick protege, at least, who got the nod. The Giants chose Joe Judge, Belichick’s special teams coordinator and wide receivers coach with the Patriots, for the job.

The news about that selection came just after the revelation that Matt Rhule, who had been regarded as the favorite for the Giants’ job, was leaving Baylor to jump to the NFL as the new coach of the Carolina Panthers. The back-to-back moves by the Panthers and Giants, on the heels of the Washington Redskins hiring Ron Rivera last week and the Dallas Cowboys completing a deal Monday with Mike McCarthy, left the Cleveland Browns with the NFL’s only head coaching vacancy.

The immediate reaction to the Giants’ selection of Judge will be mostly of the “Who’s that?” variety. This certainly is not a star-chasing move. It’s outside the box, for sure. Special teams coaches rarely are given serious consideration for NFL head coaching jobs, after all. But give it a chance.

John Harbaugh had been, mostly, a special teams coordinator with the Philadelphia Eagles before being hired by the Baltimore Ravens in 2008. (He also spent one season as a defensive backs coach to broaden his coaching experience.) Harbaugh was thought of as an equally boring head coaching choice at the time he was hired. That has worked out pretty well: He has one Super Bowl win with the Ravens and has them perhaps poised for another as the AFC’s No. 1 seed entering Saturday night’s playoff meeting with the Tennessee Titans.

The special teams coordinator is the one coach on any staff, other than the head coach, who deals extensively with players from both the offensive and defensive sides of the ball. In Judge’s case, he took on the added responsibility this season of coaching New England’s wide receivers. He also was reported to be a head coaching candidate at Mississippi State, his alma mater. Judge spent eight seasons with the Patriots and just turned 38. He is said to have earned the respect and trust of Belichick, who regarded him as a head coaching prospect.

There will be much said about whether Rhule spurned the Giants first to accept the big-money offer of Panthers owner David Tepper (a deal reportedly for $60 million over seven years, with incentives that could push its total value to $70 million), or whether the Giants already were focused on Judge before Rhule made his choice. Rhule is a former Giants assistant coach and had been portrayed as the organization’s No. 1 choice. He had been scheduled to interview Tuesday with the Giants, but that interview never took place.

Whatever the timeline of the decisions made by Rhule and the Giants, it doesn’t really matter. There is risk involved with the Panthers trusting that Rhule will make a successful transition from college to the NFL, just as there is risk involved with hoping that Judge can go from special teams coordinator to head coach. Both are, to some extent, “Who knows?” hires. Judge could also benefit if the Giants add Jason Garrett, just fired after 10 years as head coach of the Cowboys, as their offensive coordinator.

The Giants’ previous two head coaching choices, former offensive coordinators Ben McAdoo and Shurmur, were more conventional. Those picks failed miserably. The Giants have missed the playoffs in seven of the past eight seasons. The NFC East could be improving, with Rivera and McCarthy now in the division. This move might work for the Giants or it might not. But it should not be dismissed, out of hand, simply because it is so unconventional and decidedly low-profile.