Hey so to keep it short, here's what I did.

I put in the Fallout 4 disc into my Xbox One and then hit 'A' to load it up and then it takes me to the fancy "Please wait' screen and then it exits the game (it does that repeatedly whenever I load it up).

What do or what should I do?

I am definitely sure that my Xbox One updates itself overnight, that the disc isn't scratched, every other game works and that there's nothing wrong with my Xbox One.