14-year-old New York Mets superfan Braeden got hooked up with a once in a lifetime experience at spring training in Port St. Lucie, FL this week ... meeting all the players, hanging in the clubhouse and on the field!

Not only did Braeden -- who is battling cystic fibrosis -- hang with guys like Michael Conforto, Jacob deGrom, Jeff McNeil and Tim Tebow ... he also got to take the lineup card to home plate (in full uniform) before the game against the Cardinals on Sunday.

Braeden and his fam got to enjoy the game from the first row, behind home plate ... but the best part of his trip happened when he randomly ran into his favorite player -- Pete Alonso -- at his hotel!!

We're told PA was more than happy to hang with Braeden, take pics and even autograph a ball for his big fan.

“He was so chill,” Braeden said about the encounter “He was just a nice guy.”