I don't think God changes. I think He is immutable. But the wonderful thing is that His Manifestation (the way He manifests) is continuously changing.
We see it in creation, we see it in Scriptures. Existence in this contingent dimension means change.
In other words: the God that we perceive "moves" constantly, but we know that this happens because we are moving, not because He is moving.
It's like the sun and the earth, in primitive thinking. We perceived the sun as moving.... but it is not. We are moving with earth.
So, for example, the way God manifested Himself in the Old Testament is different from the way God manifested Himself in the New Testament, or in the Quran. But God Himself is the same all the way through. It is just that men in the OT and men in the NT and men in the Quran had different needs and historical and cultural circumstances and different capabilities. So God manifested to men in different ways. But God Himself never changed.