Does the existence of a state with no prior time throw models we use for explaining the existing universe for a loop? Or does it even matter?
The question is a little confusing. You cannot have a state without time - a state evolves in time.
When a measurement occurs this provokes a collapse in the state through decoherence with the environment it then continues to evolve. Note a measurement is defined to be anything that actually causes a collapse, it doesn't ahve to be a specific measuring device operated by some conscious being.
Hence, at least when physically modelled, there is no prior state.
However one can speculate at what happens at the Big Bang. Since spacetime is held to have started then, a prior state again isn't possible - there is literally no spacetime in which it can occur.
There may be other cosmologies which allows spacetime to continue through this 'singularity'. One could argue since the physical world is uncomfortable with infinite anything, this is only an apparent singularity and spacetime does continue through it. In which case the state should also continue through this singularity. But this isn't mainstream.
So, the answer to your question is no.