Answer

First, I’m not familiar with any such statement by Kant. On the contrary, in Critique of Pure Reason he goes through the three types of proof and rejects each one separately. He does not reject the very possibility in principle of proving the existence of God.
And as for the claim itself, what is so strong about it? It’s really a foolish claim. And not because the claim that He is outside logic is itself foolishness. But even aside from that, even if He is outside cognition, that does not prevent proving His existence. For example, the proof that there is something that created the world, because a complex thing is not created spontaneously, does not require any assumption about God or any ability to know Him and say something about Him. I prove that there exists something that created the world. The question of whether I have a way to know it or not is irrelevant to the proof. And so too for all the other types of proofs that I know.