Well, being unfalsifiable is a strike against superdeterminism, from the point of view of science.
I'm pretty sure that it is impossible to disprove the claim that everything was fixed from the beginning of the universe, because whatever happens is consistent with the claim that that is the only possible thing that could have happened.
But that doesn't mean that you can't falsify a very specific superdeterministic theory. The theory that says that I'm destined to never utter the numbers "3", "1", "4", "1", "5", "9" is falsified by my saying them.
(I just did, so I falsified that theory.)