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12 Monkeys did this one perfectly.
You can't change things because if you undid the thing, then there wouldn't be a reason to undo the thing. If you go back in time, you are just going to do what you already did because that is in the past.
Only if the Universe is deterministic. If not, random rolls having different outcomes may completely change the course of events and decisions made by people.
Edit: I see I'm being downvoted, so I'll explain further, if the Universe is deterministic means everything will be the same any time you relive the same time segment, if not, it means even the weather can be different due to aggregation of butterfly effect of different random outcomes in the Universe, and weather being different is already big enough change to be able to influence decisions and course of events. And I'm not meaning weather in the exact same spot you time-traveled to. Even if you restored the exact same state of Universe at some snapshot, if the Universe isn't deterministic, various random events happening after that point in time can have different outcomes which will aggregate and lead to even more different outcomes in future. Weather might be different the next day and because of that you decided to hide from rain in cafe and met someone there which can completely change your life.
Nothing is truly random, including the weather. It is extremely complex and difficult to predict, but once it happens that is what happened. As long as dice fall with the exact same speed and hit the same surface in the same spot at the same angle it will always end up with the same result. The randomness of dice comes from how the very small differences influence the outcome.
Going back in time with the knowledge of what happened the first time means that either you will choose the same thing because something led to that original choice or something will keep you from interfering. Free will exists because we don't literally know the exact outcome of our actions or the things outside of our control in advance.
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
Quantum fluctuations is basically true randomness on quantum level.
https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena
Maybe this is the same as what you're saying but my issue with the idea that "You’ve already taken said actions but just didn’t know about it so nothing changes" is that it means time travelers don't have any free will once they go back in time. If that's the case, then it bring up existential concerns and that might extend to non backwards time travelers (i.e. us)
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.
Choice is one of the slight differences that can lead to different outcomes. A rock falling down a hill will always fall downhill because of gravity. An animal can choose to slow itself or even work against gravity to move uphill. Instead of gravity, there are a ton of prior experiences that will influence that choice, but choice is still a distinct part of the process.
Are you saying that even without time travel, free will is an illusion? Surely there has to be a time travel scenario, like going back 1 second in time and shaking hands, where all information is known to both travelers, and the future self would know what was done previously, and can choose to take a different action.
I'd totally forgotten about 12 monkeys. I had that VHS of this when I was 11 or 12 years old, I probably watched it 30 times and I never fully understood it. 25 years later I think it's time for me to rewatch this
Rewatched it recently, it held up really well!
I recommend undotree, which is also a non-destructive undo, but for some cases makes it easier to reach those points.