Actually, your post gave me an interesting thought, Serra. Maybe the overall perception would be improved if we *didn't* start on the mindflayer ship already infected. We could have started somewhere else, doing smaller things and taking our first steps towards adventuring. Maybe you briefly meet or catch a glimpse of some of the other party members doing their own thing along the way, like running into Astarion if you were a Baldurian. Or maybe you were a Waterdhavian adventurer planning on tackling the Undermountain through the Yawning Portal, when Gale comes and starts buying drinks on the house to diffuse a fight about to break out in the corner. All this, before the mindflayer ship suddenly shows up above, you get to see the sheer panic that overtakes everyone around you, and you find yourself powerless to stop what's happening before you get taken.
It'd also give players time to familiarize themselves with the setting before everything goes sideways. A big reason why DA: Origin's backgrounds worked so well is because of this type of concept. You got to see how things changed drastically later in the game, instead of simply being told about it. That kind of concept also subconsciously provides an additional avenue for a player to assign extra motivation for their characters doing what they do in a roleplaying sense. (Maybe the poor reception of DOS2's Act 4 would have also been much improved if we visited the area it took place in, before heading off to the Act 3 Nameless Isles. On that note, BG3 starts off doing A LOT of telling rather than showing, really.)
Though, as with many other things, the existence of the eventual Origin system makes this a much more monumental task than it should be.