There is another theory which states that this has already happened."

― Douglas Adams, The Restaurant at the End of the Universe

If you are within the universe, then determinism doesn't prevent free will in the slightest. It only screens off free will if you believe that free will can only come from an external-to-the-universe supernatural spirit (and ignore that you haven't explained how that has free will).

Non-determinism only gives you free will if you further believe that that random noise somehow gives rise to this supernatural spirit, or allows it to affect the world. For a physicalist, non-determinism actually weakens free will (though not by much).

Remember: all non-determinism can be modelled as determinism plus random input. You can factor out all non-deterministic effects as an extra input bitstream (or… probably real-stream if the universe is continuous) fed into a deterministic process.

From that point of view, non-determinism doesn't really harm free will all that much. All it means is that you're affected by another thing you don't know about, but that's already the case in every conversation you have with another human, deterministic or no.

PS I neither believe in free will nor determinism.