It seems less a religious claim to assert that the human brain is mechanistic, and simply operates using physics to perform complex operations than to assert that there is something “unknowable”, or “outside of physics” that would prevent us from being able to build a similar machine.
If there were 0 examples in the universe, I think your point would be a good one. But, given there is 1 example, I think it stands to reason that there could be more.
I could accept an argument that one might expect it to be hideously complicated, and not something we’ll be able to accomplish for a long time.
But the claim that there’s an information theoretic reason that would absolutely prevent it, would seem to make the claim that there is something metaphysical about the operation of the brain, which seems like a quasi religious claim to me.