A general manager’s first draft pick with a team means something extra. He will be tied to that player forever, and the pick says something about the GM’s thought process and risk tolerance.

Dave Gettleman and Saquon Barkley always will be connected. And now so will Joe Schoen and Kayvon Thibodeaux, the charismatic Oregon pass rusher who landed in New Jersey on Saturday morning with a hoarse voice and a $36 million dollar smile.

“Touching down it was like, it’s meant to be,” Thibodeaux, 21, said early Saturday morning on the auditorium stage inside the Giants’ East Rutherford, N.J., facility.

Alabama offensive tackle Evan Neal and Thibodeaux both were thoughtful, personable and genuine during their first meeting with the New York media.

The impressive 6-7, 340-pound Neal barely fit through the doorway when he entered. The No. 7 overall pick said he was 378 pounds in eighth grade. Thibodeaux, who was selected fifth overall, shook his head in amazement.

“One thing I take away from the Giants organization,” Neal, 21, said, “is that they are really trying to get back to that winning culture. And that’s something that I really respect.”

Thibodeaux is a fascinating prospect, though. He is a star, a Los Angeles native eager to embrace the Big Apple, familiar already with the big city from frequent visits the past two years.

He gives off Odell Beckham Jr.-like vibes as a playmaker with an electric personality whose name and face could quickly be on billboards and marquees in this area, if not around the country.

He is so natural on camera, he could host his own national television talk show right now. He had no voice for Saturday’s big introduction because he’s been celebrating his special week.

“I would say the music has just been hitting differently,” he said. “So that’s why my voice is gone, because I’ve been singing along and singing my heart out.”

It is well-documented that some teams were turned off by Thibodeaux’s overconfidence, perceptions (right or wrong) about his work ethic, and his numerous off-field endeavors.

Some evaluators have told the Daily News they specifically have concerns about Thibodeaux keeping his focus on football in New York. Two pass rushers went ahead of him to the Jaguars and Lions. The Jets, with a head coach who loves pass rushers, passed on him for a corner.

Schoen is taking some risk by staking his early reputation on such a polarizing player.

“He’s a very outgoing individual,” the GM admitted on Thursday. “He’s got a lot of personality.”

That said, Thibodeaux showed Saturday why the Giants felt convinced he could handle this: He is self-aware. And while he is going to be himself, he knows his actions must speak louder.

“I feel like one thing with me, you can’t be a guy who blows smoke,” Thibodeaux said. “I can’t be a guy with nothing to show for it. I can’t be a guy who people look at and don’t believe in, right? So for me, no matter what I say, I know I’ve got to go put in the work.”

Thibodeaux also said — when asked about some scouts criticizing his “brand” as a distraction — that he has checked his ego at the Giants’ door.

“When they handed me the playbook it was in iPad form, and me, I learn best writing,” he said. “So for me it was like the brand went out the window. The only thing I can get done now is the playbook.”

Thibodeaux even said that mentor Michael Strahan, the great Giants pass rusher, advised him primarily to “keep the main thing the main thing.”

“Football is going to be that terminal for everything you want to do after, so long as you keep the main thing the main thing,” he said.

Asked if he would prefer to have Strahan’s football career or post-football career, he answered: “They are both ridiculous, but for me I feel like I kind of want to pave my own way. He’s done the great things he’s done because of the work he’s put in. So I got to go put the work in myself and build that legacy for myself.”

Thibodeaux admitted he is “ignorant” to the Giants’ history of great pass rushers outside of Strahan and that has to “do some research” on all of the great players he hopes to follow.

He has a more pressing matter to attend to first, though, before he studies up on Lawrence Taylor, Leonard Marshall, Justin Tuck, Osi Umenyiora and the like:

He aims to acquire the No. 5 jersey number from kicker Graham Gano, who is apparently asking the rookie for $250,000 in return.

“Just know, this is real now, we’re talking real numbers,” Thibodeaux said with a laugh. “And when you tell somebody 250, I don’t know what 250 means. You forget all the zeros behind it. Things are a lot different now.”

Thibodeaux admitted the No. 5 is “something I’m pursuing” but said he respects Gano and, knowing the kicker has five kids, “there’s a whole lot of negotiating that’s going to have to happen before anything shakes.”

But he also said “the number don’t make the player; the player makes the number.” And he said he felt a genuine early connection with Schoen and defensive coordinator Don “Wink” Martindale when they met.

“You can’t fake it, you know?” he said.

Neal and Thibodeaux clearly were exhausted from all of the emotions of the past 48 hours.

“These few days have been awesome,” Neal said. “They’ve been long. But they’ve been awesome.”

But they’ll quickly have an opportunity to put their stamp on the direction of this Giants franchise. And Thibodeaux’s journey promises to be especially entertaining and impactful on how Schoen’s tenure ultimately shakes out.

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