That's a very deep question, not easy to answer, and maybe not answerable. However, one way to look at such a question is to consider perspective. From within the universe, it appears that systems evolve over time. The relative states of things change. The "static" nature of the universal wave function implies that its overall properties do not change. This does not mean, however, that from within that system, from a particular perspective, that everything is static. Rather, from vantage points within the universe, various parts of the universe certainly are in relative motion to the other various parts.
The overall wave function will have operators/properties that are conserved (like energy) overall. However, relative to your vantage point you may see things speeding up and slowing down. There is a very big difference in describing things from a localized vantage point, where things behave dynamically, and describing them from an overall perspective, from which certain properties would appear unchanging.