Congrats... almost impossible to win full custody as a father.
I know one guy personally, but he never married the woman. She was a party girl and he enjoyed partying with her when young, then she got pregnant... and truly didn’t want the kid so she gave away rights and he raised him. Great kid.
He always said when we would talk, biggest mistake I made was getting her pregnant, no way I was going to compound it with trying to marry her.
Anyway, to your point about being out of the woods, she pretty much had no contact with the kid after they split, but did show back up when he was in HS and tried to sue to get access etc. So he had to go back to court when she sobered up settled down and began regretting her life choices... He won, but still insane he even had to deal with it.
Good luck with everything.
For the record statistics show children do much better in life by every metric when raised by just their fathers than by just their mothers.... Yes kids with both parents in home do best, but a child of a single mother on average does far worse than a child raised by a single father... but laws in the US just favor mothers to the insane degree.
For the record, please provide a citation for this claim. Preferably one that takes into account financial parity.