The way Bowser kept interrupting, and Mario's part time gig as a Doctor, i wouldn't be surprised if they only managed it after the Great Kart Race Compromise brought a small respite to the Mushroom Wars...
Ehhh, I don't know if that's accurate.
It depends on a few things, firstly if you consider JPN SMB2 to be canonical or not. If we're going strictly by US games, SMW was actually the second Bowser encounter, as
SMB3 was canonically a stage production meant to embellish and lionize Mario's exploits in SMB1. US SMB2 (Doki Doki Panic) happened entirely over the course of one night as it took place in a dream Mario had.
Secondly, how does Super Mario Land fit into all this? Well, it was released only 1 year before SMW, and 4 years after SMB1, So given that 2 and 3 were not real life events, that leaves about a 4 year swath where Mario didn't really have anything on his plate. Maybe he was attending med school in preparation for Dr. Mario (1990), but even med school leaves you with time to marinate the nether rod in the squish mitten (otherwise I myself would not have been conceived when I was - my Dad loves to tell the story about how much pressure he was under studying for his med school finals while his pregnant wife was in the hospital due to go into labor any time).
Additionally, Peach was not Mario's first girlfriend. Everybody forgets about Pauline, and a man does not climb a half-built skyscraper to combat a gigantic ape for a girl whose guts he is NOT rearranging.
So I don't buy the Adultery-sending-Mario-to-Hell theory.