When building the physical device, is the Turing Machine it is required to beat also required to have a potential physical instance in the observable universe?

What I mean is, if there are (A) atoms in the observable universe, and I think of a type of question that would provably take a Turing Machine at least (10A) atoms to answer, and then build a Non-Turing Machine that answers those questions in only 1 million atoms, then a Hypothetical Turing Machine could answer the question, but no Physical Turing Machine made of (10A) atoms could be found in the observable Universe.

However, I'm not sure if this falls into the bounds of the sexed up mistakes you are referring to above, or if it doesn't.