One could imagine a memory API with infinite storage, perhaps some sort of null-terminated addresses with no defined upper bound, but it'd be different than that.
You'd need to store it, and our universe is finite, so there isn't enough room.
Much worse the universe despite being finite is already so enormous and growing that you cannot cross it, so it would be impossible to actually perform computation as even if the data exists it can't necessarily ever be moved from where it is to the site of computation - it may get further away instead despite travelling as fast as possible.
Fit on a normal machine c99 runs on.
The second you say "most computations" you stopped talking about Turing Completeness.
Wait until you find out all memory lookups are O(n^0.5) too (assuming a holographic universe)