Does God pass through time the way we do?

It depends on how you define time. Some define time as the change that occurs from one moment to another; we measure it because something changes, as a red apple decays to a yellow one over an interval. If you define time that way, then for God there is no time, because he does not change from one thing to another; he is immutable. So when we say there is no time with God, we mean in his essence, his divine essence, which does not change in any way. Now, people confuse this with time dilation. When scientists say a clock runs slower near the speed of light, or that this watch runs faster on Mount Everest than at sea level because there is less gravity there, they are talking about clocks being affected by forces, not about time itself being flexible. Time is absolute; the watch and its mechanisms are what change. So the idea that we can manipulate time, travel backward or forward, is all bunk. Where it gets complex is the Incarnation, joining a timeless being to a time-bound one, and the question of when God decided to create, since the Church teaches God had the freedom of will not to make man and was not predetermined to do so. If you insist on the word time, you could say God reached a point where he freely chose to create, but how that works within his eternity, who knows; the question carries a lot of baggage that has to be unpacked before we even know what we are asking.