If the universe simulator can solve iterative problems in O(1), then I question whether our concept of optimization is meaningful enough to it for this discussion to make sense.
There are some physical systems (mathematically, "Hamiltonians") which have this "stateless" property. However, if the time/energy uncertainty principle is true, simulating time T in O(1) cannot be possible in general unless BQP=PSPACE (the unlikely idea that quantum computers can efficiently solve any problem that can be stored in polynomial amounts of memory). See this paper: https://arxiv.org/abs/1610.09619
What if we just lack the expressiveness or the initial conditions to model a stateless universe?
A fun consequence of stateless universe would be that you can rewind, fast forward, loop, speed up, slow down time at no extra cost.