Suspension of disbelief is one thing, but generally, a good story follows the rules set in universe.
Sure, Ash carries monsters in a ball in his backpack, but if he would suddenly gain super strength and speed, that would not make sense. We suspend our disbelief and we accept that Pokémon exist, but there is no reason for ash to go super Saiyan.
In your story, we accept that time travel exist, but there is no reason why you can't go back in time to before the alien steals the scrolls.
Feels like you kinda jumped the shark too, with the sudden addition of some alien overlord.
That said, unless you're a very gifted writer, the story should serve as a backbone for the game. The gameplay should be fun, so focus on that instead of the details of the story