That doesn't follow from the given premises. I assume the hidden leg of your rhetorical enthymeme is that the universe is a Turing machine. The burden of proof for such a claim, if you want to introduce it as an axiom, is on you. And no, the Church-Turing thesis does not prove that claim.

As a postulate, I'm happy to accept it for the sake of argument. And if we assume the universe is a Turing machine then sure the existence of human intelligence proves that a Turing Machine can simulate human intelligence and therefore it's computable.

Unfortunately, as far as I can tell nothing further follows. Perhaps it's correct, but it's rather dull too.