Here is a thought, not necessarily a thought experiment, that came to me while having my morning cup of tea a few days back. It is not to be taken as being asserted as true and, indeed, I think that there are good responses that will skirt the issue, but it is fun to think about nevertheless.
If God exists outside of time, then how is it that some people speak of “in God’s good time” or wait for “God’s timing”. If we were to take such statements as true then, necessarily, all of God’s actions are tensed and in time and, hence, God is not God (or, at least, not the sort of God we thought he was). God begins to look like a creature, since all creatures are in time. If one were to deny this then how do we explain God’s actions? All actions take place at an event (that is, actions appear to be a type of event), and events are tensed (i.e. they are now, or later, or before, or after…) and hence are in time. So, if God is not in time then God does not act. Q.E.D.
Again, I do not actually think that this little argument is conclusive as there are very good responses, but I leave those to be figured out by you.