nothing ever happens

I have previously explained my problems with the "many worlds interpretation", e.g. if one considers the superposition of macroscopically different branches, one would need to know how to handle the branching of space-time geometry.
But let us ignore gravitation for now, assume a flat background, and only consider non-relativistic, simple quantum theory.
We begin with an initial state |i> at t0 and it develops according to Schroedinger's equation, at some point containing the superposition |s(t)> of observer(s) and all that; Schroedinger's cat is in a superposition of dead and alive and so is Schroedinger, if we just wait long enough.

But somebody had to set up the experiment and get it started at t0. We cannot assume a classical observer to do that; instead we have to consider this setup of |i> as just another quantum process and the experiment could have started at t0+d or t0-d. In fact, if |s(t)> is a solution of the Schroedinger equation, then so is |s(t+d)> with d being some arbitrary constant and the many worlds wave function is the superposition of all of them.
Notice that this is very different from standard Copenhagen quantum theory. In Copenhagen there is usually an initial condition (i.e. the beginning of the experiment) that selects one solution; but such an initial condition requires a classical observer who sets up the experiment.
Obviously, if the state of our system is such that |s(t)> = |s(t+d)>, for arbitrarily small d, it follows that d|s>/dt = 0, i.e. nothing ever happens in the "many worlds interpretation"; unless we consider a Hamiltonian that explicitly depends on the time parameter.
So it seems that one needs to introduce classical time and classical clocks somehow externally, otherwise one deals with a system that forever remains in its ground state, H|s> = 0.