Sure, but it is a meaningless take. It posits into existence this being with this property, when you can just as easily posit that the universe itself has this property.
But the universe can and does change. Something that is, in that most fundamental sense, does not also have potentiality. Anything that can change, that can be "other than it is," must have some potentiality un-actualized, must not fully "be," because there are some things it is not but could be (and, indeed, later will be).
According to the Bible, God also changed, in several ways. He made a covenant with Noah, he chose a people and negotiated with Moses which commandments to give them, he came down to Earth to live and die as a human, and there are probably others.
If you say these are not changes, only actions, then the same can be said of the Universe: it didn't change, the rules of physics have always been the same, it just does things according to its rules.
Being able to interact with changing things does not require changing if you're outside the things that change. For example, if you're outside of time (which, admittedly, is really hard to wrap our heads around), from Noah's perspective, you went from "not having made a covenant with him" to "having made a covenant with him," but that's only true relative to Noah's position, not yours. You have no "before" and "after" because you're not inside time.
I'm not going to pretend I have anything like the math or theoretical physics knowledge to grok the latest perspectives on whether the universe actually had a beginning or an end, or whether it goes through singularities, or any of probably a dozen other theories that I've vaguely heard of and are over my head, never mind all the ones I don't even know about. I'm not aware of any that posit the universe is truly unbound by time, though, that time is not somehow a constraint on the state of the universe such that it doesn't actually change, except from our own perspective. Is that even what you're suggesting? Or have I missed your point entirely?
I think you responded to my point, but not in a way that is convincing to me at least. If God was willing to destroy the world in a flood before the covenant, and is no longer willing afterwards, then I would say that God has clearly changed. I accept that you could posit that God was always in the same state, one where he was willing to destroy the world before the flood, and not willing after.
But this can be done for any system just as well: instead of saying that the egg was broken to make an omlette, you could say that the egg has always been in the same state: the state where it is whole before the omlette, and broken afterwards. The egg itself is a timeless concept, but we just experience it differently as time passes for us. I don't see why this argument works for God and not for my egg.
I think I would summarize it somewhat differently, that God is (as a constant state of being) willing to destroy the world with a flood whenever it is as it was in Noah's time (which criteria determine this are not necessarily known to us, except insofar as they were met then and are not met now).
So from our/Noah's perspective, that situation has come and gone, has changed, because we're bound by physics and the passage of time and cannot exist in that circumstance any longer. But from God's perspective, that world is always destroyed by flood. It may be the case that the criteria that categorize a world as "destroyable by flood" never exist in our experience of time again, and it may equally be the case that God knows this will be the case.
But God's willingness to destroy the world by flood under those criteria has not and will never change, because God's will does not change.