I figured this out while thinking about Red Dwarf. Canonically, Lister is his own father. How can his DNA remain stable across all the time loops if he's saturated his own ancestry with himself? This is the answer. It was a 1 in 2^42 chance the first time, but after that, the time loop preserves the coincidence and Lister ends up his own clone every time. He gets all his own DNA from himself every time, and then he just has to get the same DNA from his mum every time. The science is sound. It's tremendously unlikely, but in the infinity of the universe it had to happen eventually, assuming an infinite supply of time travellers banging their own mums.

You can also apply this logic to Futurama, Star Trek, and any other science fiction show with a grandfather paradox.