The underlying mechanics are just currently unknown to us
Usually, when e.g. a physical model is deterministic, we can have an assumption of some initial conditions and then evolve the system from there - even if our model's initial conditions don't exactly match the conditions we see in a real physical system, the result of our prediction will deviate a bit from the value we see in the real system. An error of prediction that results from our error of determining the precise initial conditions of the physical system.
Usually, the error in the initial conditions of the model and the error of the prediction can be approximated quasi-linearly: small initial error, small prediction error. But, when your physical system is nonlinear, as virtually all of nature is (e.g. N-body problem, turbulent fluids, weather), it can be chaotic - which means that a small initial error can produce an almost arbitrary error in prediction.
To correctly predict the state evolution of a chaotic nonlinear system from initial conditions, you need to know the initial conditions with infinite precision. (Edit: which is impossible in practice)
Randomness isn't free will, you're not making any choices. Determinism isn't free will, your choices are pre-determined. Well how exactly do you get free will then, without invoking the supernatural? You've just defined an abstract quality that's impossible to achieve.
imo it's all a category error - the physical process by which you make decisions is your free will, it just means that your choices are irrevocable.
A suitably advanced entity could do the same: consume the entirety of my life (for whatever purpose, entertainment), its trials and tribulations, as easily as I do a book or a movie. A century of time would be a small nothing to an entity who could intake 100 quadrillion fps to my 35 fps. It could "play" my life for its amusement as easily as I play a DVD.
That said, the experience of déja vu, re: predetermination, will never stop giving me the creeps.
I'm fairly rational, however. I'm sure there's an explanation that's not magical.
so just make sure our possibly illusory free will is something positive rather than another means of self flagellation (or the other way around if that's your bag), and try to enjoy the ride.