Why not?
Ultimate Causation and Proximate Causation applies to countless things. The Bible is filled with both the natural and the supernatural applying to all sorts of things. (Was Jesus incarnation supernatural? Yes. Was the birth processes which delivered the baby Jesus natural? Yes.)
An argument based on you choosing to apply a particular word and then using the definition of that word to “prove” something? Does that strike you as at all less than convincing?
By the way, I certainly consider the presence of life on earth as a powerful testimony to God’s role in creating everything I see on this planet. Yet, that doesn’t mean that I can use the scientific method to prove God’s role. (Anyone who understands the methodological naturalism of science should see the differences between my philosophical positions and my scientific positions.)