To be clear, I think that free will--by definition--cannot exist in a purely deterministic universe. Any semblance of free will in such a universe would be purely illusory. It also cannot exist in a universe where events can only ever be some combination of random events and determined events. Randomness is also not free will.
Free Will would have to be some other special category of events that is neither determined not random. We don't have a word or phrase to describe what these events would be like other than "Free Will." However, lacking the vocabulary and math to describe it does not make it non-existent.
1) Events with no cause such as the beginning of the universe or broader multiverse, depending on your beliefs or 2) Infinite regressions of causal chains if you believe that the universe or God (or a god) has always existed or 3) Some combination of the above.
In all of these, somehow there can be uncaused effects, but in 1) and 3) some causal chains can just begin existing, like free will would require.
That is not even non-existent, more like a misconception which one comes out of by thoroughly examining what "feels" correct. Like Wittgenstein said one of the jobs of philosophy is to free us out of semantic knots. I see free will such a knot arising due to our conception of a separate self from the causality, leading us to project a conception of freedom which makes no sense when examined upon.