The point is, those premises say nothing about God one way or the other, but they do raise a number of questions that shed light on the problem. Let's look at them:
1) Observed phenomena have natural causes.
What is a "natural" cause? Is "nature" limited to what we can observe? Does the existence of "natural" causes tell us what "nature" is, or how it came to be? Is God separate from "nature?"
2) Time does not change explanations for observed phenomena.
IOW, gravity will work the same way tomorrow as it did yesterday. If I read this correctly, you're simply restating the first premise: observed phenomena have objective causes -- mechanisms remain constant with time. Why this should be so, however, is not addressed.
It boils down to this: if we accept these statements to be true, their logical consequences are identical whether or not God exists. However, if we accept these premises we must also ask the elemental question: how is it that they are true? It is in that question -- not in the premises themselves -- where the presence or absence of God is at issue.