MIAMI GARDENS — The first foundational rookie pieces for the Miami Dolphins’ rebuild under new general manager Jon-Eric Sullivan were chosen Thursday night.

And it started with a shocker following a trade down from their original top pick at No. 11.

The Dolphins selected Alabama offensive tackle Kadyn Proctor with the No. 12 pick of the NFL draft’s first round Thursday night minutes after a deal with the Dallas Cowboys.

Miami selected Proctor after passing on Ohio State safety Caleb Downs, whom the Cowboys chose at 11, and then steered clear of Miami Hurricanes edge defender Rueben Bain Jr. with that 12th pick.

But Sullivan had conviction about selecting Proctor, a mammoth blocker at 6 feet 6 5/8 and 352 pounds.

“Downs and Bain are marvelous players,” Sullivan said. “I think those guys are going to be very successful in this league, no doubt about it.

“We thought Proctor was rare. His height, weight speed, production, the things he can do on the football field for a man his size, he’s an outlier. There’s not many players like him.”

In the trade with the Cowboys, the Dolphins picked up a pair of compensatory fifth-round picks, No. 177 and 180.

Proctor made 39 career starts over the past three seasons with the Crimson Tide, all at left tackle.

The Dolphins don’t need a left tackle, as they have one of their potential franchise cornerstones there in Patrick Paul, but at Proctor’s size and with the power in his game, he is believed to possess positional versatility to also play guard in the NFL.

“He’s a 350-pound man with unique athletic traits that can play four spots across the line of scrimmage, the left tackle, right tackle, both guards,” Sullivan said. “The athletic traits for a man his size are through the roof.”

The pick holds true to the belief the Dolphins want to build from the inside out. Proctor can move defenders in the run game for speedy tailback De’Von Achane, who is expected to receive a contract extension later this offseason, and can help protect new quarterback Malik Willis.

“I know that we’re going to run the s— out of the ball,” said Proctor, who can play with a mean streak when bulldozing defenders standing in his way. “That’s O-line play. It’s physicality. You’re trying to put the man on the ground, move a man against his will. That’s my favorite part about the game.”

The selection also shows a belief Miami’s offensive staff thinks Proctor is athletic enough to block in the outside-zone scheme.

“I feel great about it,” Proctor said. “As I keep the weight in check, I believe that I can play all 60 minutes as fast as I can and really just be that fast, physical, explosive guy that I know that I am and just using my skills to my advantage, going out there and playing fast and free.”

His weight has been deemed a concern, even by former Alabama coach Nick Saban, who coached Proctor as a freshman. Saban told Pat McAfee Show that Proctor can grow overweight when not in the team’s building.

“I know there’s been some questions about his weight,” Sullivan said. “It’s well-documented and, obviously, we’re very aware. We did our due diligence with our resources. We feel really good about where he is at with that.”

Drafting Proctor also gives Miami the option to kick him out to right tackle in the future if the team moves off from Austin Jackson. In the meantime, the team may have a decision to on whether to play Proctor or Jackson at guard.

“I feel comfortable playing anywhere,” Proctor said. “Whatever I can do to put my team in the best light to go win games, I’m going to do whatever coach tells me to do and go out there and provide for the team in any way I can.”

Aside from Paul and Jackson, the Dolphins have a key building block on the offensive line in center Aaron Brewer.

Guard is a big question mark for the team, as the team hopes for development from Jonah Savaiinaea, the previous regime’s second-round pick who was traded up for in last year’s draft.

The Dolphins signed former Chargers lineman Jamaree Salyer, who can play guard and tackle, and swing tackle Charlie Heck among their free-agent additions.

After picking Proctor, Miami moved up with its later first-rounder, from No. 30 to 27 with the San Francisco 49ers, to select San Diego State cornerback Chris Johnson.

“We were convicted on these guys,” Sullivan said. “I really like what we did (Thursday) night. … I think the Dolphins got better.”

On Friday, they select at No. 43 in the second round and then have three third-round choices after trading one of their third-rounders to the 49ers. They picked up a compensatory pick from the 49ers in that deal, and the two fifth-rounders acquired from the Cowboys give Miami a total of seven Day 3 picks between the fourth and seventh rounds.