A clever DM could pull off starting a level 1 campaign in the Underdark. I'll have to check out the module mentioned. But it would be very tricky, imo.
The Underdark, regardless of the milieu, is supposed to represent among the most deadly environments anywhere. It is universally inhospitable to humans, most unwelcoming, and often utterly alien. For a level one party to survive to the point where they could start venturing forth in the general environs of the Underdark at large, they'd have to be sheltered in some city that is either friendly to humans/demihumans or at least allows them the freedom to adventure within a very controlled environment in order for them to gain experience and levels.
If, however, the adventure in question just throws them into the Underdark wilds willy-nilly, than any depiction of that adventure is going to be one in denial; although a lowly party of inexperienced adventurers might make it a few if not even a few score miles, presumably upwards towards the surface, no version of the Underdark should be without a genuinely lethal encounter just around the bend consisting of any number of capricious or simply ravenous creatures ready to enslave or consume or rend our intrepid noobs into strips of red flesh.
If BG3 tries to pull this off, Swen had better tread carefully. You just don't mess around in the Underdark.