I'm talking about particles at the quantum level here. Subatomic particles are ridiculously small. The amount of empty space in the universe is incomprehensibly vaster than the amount of particles that inhabit it, so it wouldn't be surprising to me if it were impossible to arrive at the same universe-wide state from different starting points, but I don't know that that's true as a matter of fact. But if there were a perfectly symmetrical perturbation, by definition it would be unobservable to us, since we would end up in the exact same state along either pathway.