Initial value setting errir

Your waveform does not show what you are saying in your post. I just see state as unknown or don't care throughout the sim.

If you are really trying to build an FSM, this is not the way to do it. You need two processes: one that is usually a clocked process (you have no clock here) that handles state transitions, usually based on input signals or the current state and one process that handles what the outputs should be when in a particular state. It's unclear what you're trying to do here.