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.
I believe it’s impossible in the real universe.
Sure there are solutions of general relativity that contain time loops, but they require stuff like an infinitely long cylinder, or escaping a spinning black hole, or negative energy. I just don’t believe beings made of finite matter and with finite energy will ever be able to time travel (except into the future at various rates) and that’s the only kind of beings I think exist.