Causal Loop. It's an actual scientific thing. Also known as a
Bootstrap Paradox.
You must be registered to see the links
It's pretty common in science fiction. A notable example is the Terminator franchise. If Skynet didn't try to prevent John Connor from being born, his protector wouldn't have been sent back and put into a position to become his father and John Connor wouldn't have been born. There's other stuff in that franchise that's a bit messy with its time travel stuff too, but that's the inciting event of the franchise from the audience's perspective.
I don't think I've seen a movie or read a story about time travel I haven't had problems with. Time travel is just really difficult and you kind of just have to ignore stuff and just enjoy the ride.