Is Goedel's 1st theorem not algorithmically derivable?
Your reasoning is incorrect.

It is true that your hypothetical "proof deriver" cannot derive all true statements. No proof derivation system can, and indeed, it is not even possible to express the set of true statements in arithmetic, which is a consequence of Tarski's theorem on truth, itself a consequence of Gödel's theorem.

However, your algorithm does enumerate all provable statements, including the incompleteness theorem itself.

In fact, here's a much simpler algorithm:


Print a formal proof of the incompleteness theorem.
Halt.


So you need a much subtler argument to prove that computers can't do what humans can do in terms of proofs. Certainly you would need a better notion of what "prior knowledge" of a proof means. Indeed, many people today believe that there are no tasks which are fundamentally impossible for computers but possible for humans, and I know of no unassailable argument for that position.