They started with Strange Worlds, TTA and TOS #1. All on sale around the same time.
What about Strange Tales #70? What was the date on that book?
It seems to me that the earliest TOS were more sci-fi oriented, and even a book like #5 isn't quite a monster cover in the sense of the giant "monster of the month" books they'd do a bit later (TOS #6 gets my vote for the first of those in that title). TTA #1 has a giant monster on the cover, but more of a King Kong vibe (to me, anyway) and while the cover to #3 sort of fits that bill it too seems more sci-fi. #5 is getting there, and #6-7 are definitely there, IMHO. JIM may have a good case for earliest, as books in the early to mid-50s (I mean numbers, not years here) are making that transition from Sci-fi, to big Sci-fi creatures, to big monsters like Hulk and RRO! Look at the evolution from JIM #52-56 or so and it's a microcosm of the shift from sci-fi to "monster of the month".
Strange Tales 70 was on the stands with Strange Worlds 5. I stand by what I said.
Makes sense too....TOS and TTA sported ALOT of big monsters on the covers.
Strange Worlds #3 could make a claim as an early example, but it is buried amidst four other sci-fi covers, not "monster of the month" covers.
ALL the "big four" pre-hero books had a lot of monsters, but the question was when they started. Strange Worlds (aside from maybe the aforementioned #3) and the first five issues of TOS and TTA don't really follow that pattern, IMHO.