Given the complexities of DC's multiverse it is impossible to say exactly what Earth's continuity (retroactively) "The Mightiest Team in the World" occurred in.
This being the first team-up between Superman and Batman, would in theory, exclude Earth-Two as those versions of Superman and Batman met years earlier, as members of the Justice Society of America and All-Star Squadron.
The official sources Who's Who: The Definitive Directory of the DC Universe #2 identifies Detective Comics #327 (1964) as the first appearance of the Earth-One Batman and Convergence #0 cites Detective Comics #327 as the first appearance of "Pre-Crisis Earth-One Gotham City" so where ever "The Mightiest Team in the World" happened it is certainly not Earth-One.
This leaves two official alternatives: another Earth entirely or a hypertime distorted Earth-Two. If it is another Earth is it most likely Earth-Two-A as it fits the general criteria: an Earth-Two Superman story of the 1940s through 1950's with Earth-One elements (Earth-Forty which has similar Earth-Two + Earth-One elements does not have this issue listed as an appearance so by official sources it is effectively eliminated from consideration).
In any cases saying that this issue is the first appearance of the Earth-One Batman is not supported by any official source effectively making it fanwank in designating it as such.--BruceGrubb (talk) 12:21, September 16, 2017 (UTC)