I don’t think there is an axiom 2. If you would like to propose another sort of knowledge (or, more correctly, another way of gaining knowledge), we could consider it. But why is that other way, whatever it is, apparently not usable in science?
On the other hand, if natural theology is possible using only the methods of science, I’d like to see that done. I would agree that it’s possible, but the results would not be positive for God.