Let me first address what happens when you try to grasp free will "as a solid experimental fact". I will then also go on and provide a physicist version of a classical philosophical argument about free will in a wider cosmological sense.
Let us define pure free-willness of a phenomenon as the extent to which it is independent of initial conditions (or the completely idealized preparation of the system, possibly including a human). I.e., your choices are determined by circumstance and motivation, but if we want to have purely free decisions which cannot be planted into our minds from the outside, there must be a factor X which is not determined by any conditioning.
Now take a look at it from the point of view of the scientific method: would any empiric construction of a theory be able to distinguish between free-willness and randomness? No, it would not. Pure free-willness and randomness will be the same thing in any strictly scientific theory. There might be an ontological distinction between free-willness and randomness, but it is not, by its very definition, accessible to the scientific method.
So, theories which allow for the ontological postulation of free will are those which, at least for now, contain a fundamentally random, undetermined element. This was also the basis of the idea of Roger Penrose to somehow link the element of randomness in quantum mechanics with the free will of the human brain.
However, there is a loophole which allows for free will even in a purely deterministic theory, and that is to zoom out on the whole cosmology and realize that the scientific method fails at that level. There is no experimenter which determines the given conditions in the universe to test the outcomes. Even if someone, in a monstrous hypothetical scenario, were to raise and "program" a child to a certain behavior, they would never have complete control of their conditioning. If, then, you erase the extremely conventional and arbitrary distinction between "an individual" and "their environment", the behavior of the child has the same "freeness" as its conditions.
To give a concrete example: you go to your favorite bakery to buy a croissant and the baker Jacques smiles at you while handing you the croissant. You may ask yourself: why did Jacques smile at me today? And you might say: well, because it was a sunny day and he knows me since I have been going there, also he is a human and as a typical human he likes sunlight and company, and humans have developed like this because... This allows you, in principle, to construct a deterministic chain of argumentation, but ultimately does not allow you to explain why these unique conditions determining Jacques' smile have come to be.
Getting a little bit more into physical terms, if we believe that the evolution of the universe is in some sense "unitary", that is, no new information is created by the time evolution, Jacques' smile has always been "out there" in the initial conditions of the universe. But the initial conditions of the universe are undetermined by the scientific method or any physical law in the classical sense. You can thus say that these initial conditions are "free". In this sense, if you ask about Jacques' smile in a cosmological frame, it is as free and undetermined as can be.
(I just want to repeat that I very much realize that this is a notion which is strongly different from the intuitive idea of free will of the totally distinct individual vs. the totally distinct exterior universe.)