Long before front-office executive Adam Peters was helping the 49ers sign players, he was trying to get one of their greatest players to sign his game program.

The problem? Peters was a 7-year-old die-hard who was overwhelmed when Joe Montana, sidelined after back surgery, shared an elevator ride with him and his mom at Candlestick Park in 1986.

Peters frantically fumbled with the pages, trying to find Montana’s picture, before thrusting a random page at the legend. Peters, now the 49ers’ vice president of player personnel, recalled his reaction to the unexpected sight of Montana, whose poster hung in his bedroom in Cupertino.

“I said, ‘Holy,’” Peters said, before pausing to edit his memory. “I didn’t say, ‘Holy s—,’ because I didn’t swear then, I don’t think. But I was so nervous and scared that I couldn’t find (the page), so my mom was just like, ‘Just give him the sheet.’”

Thirty-one years after he got Montana’s autograph, Peters, 38, got his dream job in January: General manager John Lynch made the Broncos’ director of college scouting his first hire on Lynch’s second day on the job.

Peters grew up in Cupertino during the 49ers’ dynasty days. Now, as Lynch’s right-hand man, he’s a powerful figure in a regime tasked with finding the next Steve Young (Peters got his autograph at a training camp) and Brent Jones (the tight end whose jersey number — 84 — Peters wore in high school and junior college when he played the same position).

Unlike Lynch, who played for Bill Walsh at Stanford, and head coach Kyle Shanahan, whose, dad, Mike, was the offensive coordinator on the 49ers’ last Super Bowl team, the masses can relate to Peters’ connection to the franchise.

That is, he was a fan. And, in some ways, he still is: His office walls feature pictures of the Big 3 (Montana, Young and Jerry Rice) and his favorite player (Jones).

What’s it like to work for your childhood team? Just listen to Peters, who began detailing his first months by sounding like a certain awestruck 7-year-old.

“My first day, I met (former 49ers linebacker and current team employee) Keena Turner,” Peters said. “My family loved Keena Turner, and I love Keena Turner, too. I get to see him every day. So that’s really cool.”

Hear Peters discuss his childhood passion long enough and it’s easy to forget he’s one of the NFL’s top young executives and owner of three Super Bowl rings from his tenures with two marquee franchises: New England (2003-08) and Denver (2009-16).

Peters, who broke into the NFL at 23, leads the 49ers’ personnel and scouting department and is listed above ex-Lions general manager Martin Mayhew, a recently hired senior personnel executive, on the masthead.

“Will Adam be a general manager one day? Yeah, that’s a no-brainer,” said Cowboys director of college scouting Lionel Vital, 53, who spent two seasons with Peters in New England. “He’s smart, he works as hard as anyone in the building. He can read people, including players, has a great understating of the game and is an independent thinker. Right there, those are a bunch of traits that the top GMs have.”

Lynch, who had no previous executive experience, made hiring Peters his first transaction.

Why Peters? In 2013, Lynch, then a Fox broadcaster gauging his interest in front-office work, spent a month sitting next to Peters, then a national scout, in the Broncos’ draft meetings. Lynch was struck by how general manager John Elway and director of player personnel Matt Russell valued Peters’ input.

“In certain rooms, you can tell when certain people are allowed to speak and Adam was one of those guys they wanted to hear from,” Lynch said. “I remember saying to John, ‘Hey, this guy’s good, huh?’ And he said, ‘Oh, yeah, very good.’”

Lynch didn’t interview Peters before he hired him. Beyond his firsthand experience, he’d heard others rave about Peters when he traveled around the league for Fox. And Peters’ boosters included one of the best coaches in NFL history.

Bill Belichick kind of gives praise grudgingly,” Lynch said of the Patriots’ head coach, “and he thinks very highly of Adam.”

Peters has helped Lynch with the mechanics of organizing a draft board and other minutiae that were foreign to the rookie executive. But Lynch, whose 15-year playing career included nine Pro Bowls, valued Peters mainly for his player-evaluation skills.

Peters’ influence was felt before he joined the 49ers. After Lynch received permission from the Broncos to speak with Peters, he called him and asked about the upcoming draft: “We’ve got the No. 2 pick. Who are you taking?”

Peters’ no-hesitation response: Reuben Foster.

Coincidence or not, Lynch became similarly smitten with the Alabama linebacker. The 49ers say they had Foster third on their board even as predraft injury and character concerns hurt his stock. The 49ers traded up three spots to grab Foster with the No. 31 pick. Foster doesn’t come without risks, but Peters is confident his passion for football will lead him to make the “right decisions” in his career.

“It’s not just identifying talent,” Vital said. “It’s identifying what makes that talent tick. Adam’s very good at that.”

Peters is also adept at working. And the path to his dream job was paved with perspiration.

He credits his work ethic to his dad, Fred, an engineer at Yahoo, and his mom, Laurence Mongiello, who recently died and had worked as a teacher and guidance counselor.

Peters attended Monta Vista High in Cupertino and was an all-conference tight end at West Valley College in Saratoga. On-field success didn’t follow him to UCLA, where he was an undersized, nonscholarship defensive end who received scant playing time. But his work ethic was unaffected.

“There were some limitations, but you couldn’t tell him that,” said Don Johnson, his position coach at UCLA. “I think Adam’s desire is what got him into the position he’s in today.”

Randy Taylor, who helped oversee UCLA’s recruiting, created a position for Peters in the recruiting office after he graduated in 2002. And Peters quickly made the most of it. He hosted Patriots executives Scott Pioli, now the Falcons’ assistant GM, and Jason Licht, the Buccaneers’ GM, and impressed them so much during the on-campus visit that he was hired by New England five months later.

“I always want to work with the walk-ons,” Taylor said, noting Peters retained the drive he displayed as a player. “Those are the guys that become (executives with) the 49ers.”

When Peters became an executive with the 49ers, his family celebrated as if their team had won its sixth Super Bowl.

His younger sisters, Joanne, 34, and Stephanie, 32, sported 49ers cheerleader uniforms in childhood. And Joanne struggled to wear another team’s gear during her brother’s previous NFL stints: She wore a 49ers T-shirt underneath a Broncos jersey that Peters had given her when she saw the 49ers play in Denver in 2014.

“I love my brother and I want him to be successful,” Joanne said, laughing. “But we’re 49ers faithful.”

His family will keep cheering, but Peters can’t be much of a fan as he labors to help rebuild a once-proud franchise. However, he hopes the grueling task comes with a personal perk: the chance to visit with Jones and Montana, the heroes he’s yet to meet since he was hired.

If he does sit down with Montana? Peters plans to mention their meeting 31 years ago.

“I’m sure,” Peters said, “he remembers it just as well as I do.”

Eric Branch is a San Francisco Chronicle staff writer. Email: ebranch@sfchronicle.com Twitter: @Eric_Branch

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