Will Tye couldn’t get off the bench at Florida State and wasn’t even invited to the NFL Scouting Combine last winter.

Last Sunday, the Stony Brook University product was catching key passes in a close game against the defending Super Bowl champions.

Yes, to say the Giants’ rookie tight end took an unconventional path to the NFL would be a massive understatement.

“I feel like I’ve been walking around in a big fog because it’s so unbelievable,” Tye said this month. “But I’m loving it. Every minute of it has been a thrill so far, because it feels like I’m part of something special.”

The Giants, in return, think they might have stumbled on a diamond in the rough in the undrafted Tye.

The Middletown, Conn., native was promoted from the practice squad in October out of desperation — Big Blue was running out of tight ends because of injury — but has made that move look savvy in seven appearances.

Tye is coming off his best game as a pro in last week’s 27-26 loss to the Patriots, with five catches for 56 yards that included a 31-yard catch and run just before halftime that set up a touchdown.

Tye has had some drops but is a contributor with 15 catches for 152 yards in seven appearances overall, giving the Giants production they weren’t expecting after tight ends Daniel Fells and Larry Donnell were lost to injury early in the season.

“The game is not too big for him,” Giants offensive coordinator Ben McAdoo said last week. “He seems to play with a calm mind, plays at a good speed, [has] soft hands, and when there’s a lot of moving and shaking going on out there, it doesn’t seem to disrupt him much.”

Pro football didn’t seem like such a pipe dream for Tye as recently as 2011, when he was a four-star Florida State recruit with visions of stardom dancing in his head.

Tye quickly found out he was just a dot in the sea of talented recruits in Tallahassee, including one at his position — current Bills practice-squad member Nick O’Leary — who kept Tye nailed to the bench en route to winning the 2014 John Mackey Award as the best tight end in the country.

Tye was long gone by then, though, having transferred to Stony Brook the year before after realizing his hopes of an NFL career weren’t going to happen if he couldn’t get on the field in college.

The move to Long Island paid immediate dividends, as Tye caught 79 passes for 1,015 yards and nine TDs in two seasons for the Seawolves, earning second-team All-Colonial Athletic Association honors as a senior.

That wasn’t enough to get the 6-foot-2, 262-pound Tye an invitation to the scouting combine in Indianapolis, however, leaving him to try to make the NFL a reality by way of his pro day and the dreaded nationwide tryout route.

The Giants were one of Tye’s tryout teams after they saw him run the 40-yard dash in 4.47 and 4.50 seconds at his pro day. Those two times would have made Tye the fastest tight end at the combine if he had been invited and replicated them.

Tye was among the last players cut by the Giants out of the preseason and feared he would be mired on the practice squad until Fells and Donnell went down, prompting the call from the Giants that no one would have predicted as recently as the run-up to the NFL draft last April.

“I always felt like he had it in him to be a good player,” Giants tight ends coach Kevin M. Gilbride said of Tye. “He’s young, he’s green, his development is what still needs to take place, and it shows.

“But I’ll tell you what,” Gilbride added, “he’s made some big plays for us, too, and I think down the stretch, he’s going to make a lot more.”