9:35 AM PT -- The fan -- Alan Alcantara -- tells TMZ Sports the move wasn't as risky as it seems ... explaining there is a floor in center field that wasn't visible on the broadcast footage.
"It was not like there was a hole there where the kid was going to drop and die," Alcantara said.
He added that it wouldn't have mattered anyway ... telling us his grip on his babies is just that strong!
An MLB fan terrifyingly leaned over some railing with his baby in his arm to try to catch a home run ball on Tuesday -- but, thankfully, he avoided disaster, made the grab and kept everyone safe!
The wild moment went down in the first inning of the Washington Nationals game against the Mets in New York -- when Starling Marte crushed a home run to deep center field.
let's go babyyyyyy pic.twitter.com/rXqpiJ002Y— Cut4 (@Cut4) May 31, 2022
let's go babyyyyyy pic.twitter.com/rXqpiJ002Y
The ball landed in an area with no seats, took a huge hop -- and that's when a dad in the stands made a play that we're sure Mom wasn't too pleased to see.
Broadcast video from the game shows as the ball was coming back down from its initial carom, the man held his baby with one hand and made the barehanded catch.
"Did he catch that?!" the game's announcers asked. "Baby's fine! All good!"
The fan actually spoke to the Associated Press about the play following the game ... and revealed he was a former baseball player -- so the catch was no sweat.
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"In Dominican Republic, we don't all get to have gloves, so we do play baseball barehanded, so I figured I could do it," the fan said. "I did it many times when I was a kid, so why not?"
The kid, meanwhile, was totally fine.
As for the man's plans for the now-famous ball ... he said he's giving it to his pastor, who's a huge Mets fan.