On PC it's the vault key (E), although in this case you're technically using it to mantle. I don't know what it is with gamepad, but it should say in the controls menu.
You must have used shoot dodge dives to get over the rooftop ledges in New Jersey like I did my first play through. When I found out there was a key to vault/mantle things, I felt so dumb for wasting bullet time. Guess I was too anxious to play the game to look at the controls menu thoroughly.