Determinism comes in a couple of flavors, one of which is "chaotic". I think that most interesting behavior lives under the header of "chaotic". Insofar as we experience free will, I think it's chaotic behavior.
I think time loop stories are one of the gateway drugs to this mode of thinking ( a time loop thought experiment is an easy way to say "repeatedly resetting the world to a known set of parameters") .
In these stories; when the protagonist goes back in time, (s)he doesn't get knocked over by people robotically acting out what they did in the time loop. But neither do events unroll completely at random.
Instead people react to the protagonist's actions, and then other people react to their reactions, etc. So what starts out in one corner with the protagonist arriving with their time machine will spread out to affect everyone else's behavior over the next few days. After a week or so this effect has spread out such that the future of this particular time line is no longer easy to determine.
Chaos is a funny thing. It's technically deterministic, but can sometimes feel like randomness.
Time loop stories themselves aren't real. But they make an interesting thought experiment that gives one an intuition on (how I think) the world works.