I don't know enough about either one of them, but my best guess from what little I know is that if they're not entangled, then that might be because the singularity didn't have the same characteristics as photons and atoms and stuff that allows them to be entangled in the first place and I think it it can only happen in some certain kind of situation too. Either that or they can become untangled if they did entangle in the first place.
EDIT: Also, I thought the Big Bang came from some singularity thing that was as dense as all the matter and energy in the universe (maybe more) and eventually became a bunch of different particles later on, so it didn't even have anything to entangle with. Sorry if my ignorance is showing, but it's still fun and interesting to talk about and I might learn something here.