For P vs. NP to apply, you would have to be given a Turing machine (or equivalent program) that could verify a guess in polynomial time, without having to ask s

For P vs. NP to apply, you would have to be given a Turing machine (or equivalent program) that could verify a guess in polynomial time, without having to ask somebody. But how do you know that Turing machine couldn't be somehow reverse-engineered to find the number without trying every possibility? You don't know, you're just assuming it. Proving that assumption is the entire point of the problem.