It seems that Alan Moore came up with 616 for the main Marvel Universe. Whether he pioneered the concept entirely is less clear.
This extract from The Official Handbook of the Marvel Universe vol 2 explains why 616 was chosen for the main Marvel Universe:
Numerous theories as to why that specific number was chosen have proliferated across the net since then, ascribing various hidden meanings to it; however we recently asked his daughter Leah Moore and her partner John Reppion if they could ask Alan and solve the mystery once and for all, which they graciously did. The response: 616 “was just a random number of no significance chosen because people always seemed to be talking about ‘Earth 2’ or ‘Earth 4’ but never any higher numbers.”
This suggests that somebody else invented the numbering system before him. But there’s no detail on where he saw these other numberings: it could have been another comic artist, a fanzine, or an entirely different comic universe.
I would guess that he probably wasn’t the first to use numbers to distinguish universes in the Marvel canon, but I also don’t know who did, either.