Science fiction is as old as fiction. The Epic of Gilgamesh (2000BC) and Ramayana (500BC) have sci-fi elements. There's nothing innovative or unique about stories that imagine a future instead of a past, present, or alternate reality.

Genres are too vague and generic to be ownable by anybody. Inspiration is not plagiarism.

There is some LLM trained only with old content, maybe someone can describe a style invented after the more recent content and told the AI to do a novel with that style and see what the result is and compare it to the "real" style.

I think you mean if AI was never trained on science fiction, would it ever be capable to produce science fiction and the answer is probably not. At least LLMs need a huge body of training to produce derivatives

As far as I am aware AI wont write/do anything without an input prompt.. or has something changed ?