If determinism were true, then since each state could be project from the initial state, we could simply suppose that the whole four-dimensional shebang came into existence causally "all at once", so that there would be no causal relations within the four-dimensional universe. The only relevant causation could that of God's causing the universe as a whole--and an atheist might just think the four-dimensional universe to be uncaused.
I think that this acausal picture could be adapted to give an attractive picture of the role of causation in a collapse interpretation of quantum mechanics (whether the collapse is of the GRW-type or of the consciousness-caused type). On a collapse picture, we have an alternation between a deterministic evolution governed by the Schroedinger equation and an indeterministic collapse. Why not suppose, then, that there is no causation within the deterministic evolution? We could instead suppose that the state of the universe at collapse causes the whole of the four-dimensional block between that collapse and the next. As long as collapse isn't too frequent, this could allow occasions of causation to be discrete, with only a finite number of such occasions within any interval of time. And this would let us reconcile quantum physics with causal finitism even with a continuous time. (Relativity would require more work.)