Simply put, I've gone through a large chunk of act one and I feel as though the game has done little to nothing to really introduce me to the setting of Faerun.
Or 5th Edition D&D for that matter. As I said elsewhere this is a generic Larian RPG with a very THIN layer of D&D whitewash, while advertising as much more so.
I think this is partially WotC's fault. The storyline picks up right after Descent Into Avernus, which was a problematic module at best. Many theorise that Baldur's Gate itself was supposed to be dragged into Avernus, but WotC chickened out and made it Elturel instead. The whole first act of DIA is set in BG for no reason, other than people love/have heard of BG. So Zevlor telling us that they're refugees from Elturel means almost nothing.
Even then, I can't think of any 5E module that does a good job of taking advantage of the setting. Faerun really hasn't gotten a lot of love in 5E, we have a little on the Sword Coast and that's it. Not saying Larian can't do better, but remember they're doing this with WotC's involvement and blessing, such as it is.
The narrative around both 4e and 5e is rather questionable/difficult in my opinion. Most of the world environment makes sense to me because I played the AD&D and D&D2e games tabletop, as well as D&D2e and D&D3e on PC. The history and geography are still the same ( well, not all the geography ), the monsters races and classes are all just about still recognizable, so I only need a few blanks filled in, which the game does well with books and conversations focussed around the salient storylines.
I think it would be hard to give a worldview that ALL characters would know; anyone from Baldur's gate, regardless of race, would have a certain body of knowledge, but a Drow, say, just up from the Underdark would have a completely different background knowledge. Even within a race, the understanding of a sage or noble would be very different from a thug or urchin.
If Larian do want to add immersive background flavour, I think an extensive book list is the easiest route. It does not require the level of resources that conversations would require, and reading books is elective, so the player can choose what to learn about.
As I'm sure most people know already, WolfheartFPS, the youtube streamer that appeared in PFH 5 has a narrated playthrough of the Descent into Avernus 5e module that directly preceeds BG3. I found that very useful for setting the immediate background of BG3.