I think from a physics standpoint, strict free will is already an illusion and the only useful definitions of free will basically boil down to "choices can be made", perhaps as far as "Slight differences in initial conditions can lead to different choices" (but somehow excluding random processes). That kind of definition doesn't even require consciousness, and is compatible with a deterministic universe like ours seems mostly to be. Would also be compatible with the time traveler unwittingly doing everything as must happen, but still via individual choices.

Let’s suppose a time travel event occurs in which an agent with free will travels to their own causal past, and let’s suppose this creates a parallel timeline which can differ from the first (leading to a new version of the agent which creates a third timeline, and so on).

We can consider this time-travel event as a function in which one timeline maps to a successor timeline — or in general, the event is an iterative map from the space of possible timelines to itself. If this map meets a few general criteria, we can apply the fixed point theorem and conclude that, after enough iterations, the process will converge to some fixed point that maps to itself (that is, the agent causes the past of their own timeline, even though they have free will). This timeline maps to itself—but it is also mapped to by an infinite succession of timelines in which the agent is free to alter their successor timeline, converging on one in which their choices cause no further alteration.

At that point, we can dispense with the assumption that time travel creates parallel timelines, and assume instead that the fixed-point, self-causing timeline is the only real one.

Nothing is truly random

Modern physics says otherwise. Einstein also thought exactly like that with his "hidden variables" theory which was later disproven.

Edit: I was interested to read some relevant discussions and here's some links with quotes

https://philosophy.stackexchange.com/questions/29364/does-true-randomness-actually-exist

https://physics.stackexchange.com/questions/651011/is-there-quantum-randomness-that-significantly-affects-our-macro-world

It seems very likely that every deviation from perfect homogeneity and isotropy in the universe is due to amplified quantum fluctuations. (That's true in inflationary cosmology, and I'd expect it to be true in practically any alternative to it.) For example, the shape of Earth's land masses was probably determined by quantum fluctuations, and has had an enormous influence on human history.

Quantum fluctuations is basically true randomness on quantum level.

The randomness is largely canceled out, except in the case of unstable systems which magnify the effects of any perturbations, no matter how small.

https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena