Here's a dumber argument: suppose you simulate a Newtonian universe in a computer. We do this at a coarse scale all the time. Now, suppose we dedicate a few percentage of solar output to this project and out pops functioning artificial life that can think more or less like we do. Such an "organism" would be able to discover Gödel incompleteness just as well, and thus eventually conclude via the same chain of logic as this paper that the simulation hypothesis is false. While inside a simulation.

Sure, I'm assuming here that nothing Gödel's brain did is fundamentally non-computable, but that's a pretty easy lift I think. Math is hard but it's not that hard.

For what it's worth, while I find this "obvious" as well, given the Church-Turing Thesis etc, Nobel Prize-winning physicist and philosopher Roger Penrose famously does think that human brains require access to non-computable insights to do math.

He, however, seems to hold the minority view under Nobel prize winning physicists on this subject.

appear to the a-life Moses with tablets with the non-simulation proof written in Lean. They don't need insights to verify that proof, just a computer running inside the simulation.

Or just start simulating QM on a limited basis, just inside their brains. You might need to run evolution for another few million years until they start taking advantage of whatever Penrosian effects there are.