When I was younger I remember always being pissed at those movies with the typical circular logic time travel loop: The protagonist is convinced through some event to travel back in time. They end up causing the events which convinced them to travel through time in the first place and ultimately either couldn’t or wouldn’t change the past. I thought this was paradoxical, because it relied on circular logic, and if at any point the protagonist broke the chain they could’ve changed the past and the whole movie wouldn’t make any sense.
But then I watched Dark (which I loved, until they ruined it with a feel-good ending about being able to change your fate), and it occurred to me that time loops aren’t necessarily paradoxical. After all what’s stopping the existence of a loop where everyone agrees to and somehow serendipitously does everything right in order to make the loop self-consistent? All it requires it everyone in the universe is either unwilling or unable to change their pasts.
As for what happens if anyone in the universe is willing or able to change their past, the answer is simple: Such a universe could not have existed in the first place. Therefore by the anthropic principle, the only time loops that can exist, are those were everyone is unwilling or unable to change it.
For this same reason, it’s silly for time travel protagonists to worry about causing a paradox, because if they were able to cause a paradox the entire universe they inhabit couldn’t have existed in the first place. Then again, it's also fair to say that their illogical worrying is what allows that whole universe to exist in the first place. Just know that if time travel were possible in real life, you wouldn't need to worry about causing a paradox, because the fact you and your universe exist guarantees it's logically impossible for you to cause a paradox.
Remember: A time loop cannot change over time! Imagining a time loop as a looping video where people can change over each iteration, and/or winking in or out of existence “over time” (like the end of Dark) is illogical because a time loop already includes time.
Note: Regarding the idea it's paradoxical because you don't know what "caused" the time loop itself: I think this stems from a misconception that a time loop can be caused or created at some point in time, rather than simply existing. The concept of cause and effect only make sense within a causal chain. If you ask what caused a causal chain itself, it's naturally unanswerable, just like the question of what caused the first cause of our universe. Here is the reddit argument which inspired this post.
Note: this post purposely ignores the “branching universes” model of time travel because it’s a cop-out that avoids all paradoxes trivially because you don’t need to tie together any loose ends.
