my suggestion might be quite simple to formulate and i wonder it might have been many times suggested already, but i suppose that it might not be as simple to implement... Nevertheless It correlates with on-going development of changing civilizations mechanics, so I do really hope that we might see it one day in some git update
When player receives a message with possibility to switch to a new civilization - the new civilization already exists on the map and AI already ended its first turn. It sometimes really irritates as for example in some cases it is better to found capital in different places, but AI makes it right in the 1st turn, right at the place where its settler is appeared.
So, basically, my suggestion is to shift this switch dialogue window by 1 turn earlier and ideally try to unify the switch mechanic output with the result that you would see if you have just started playing for the new civilization from the beginning of the game without switching (dialogue about newborn civilization\civ-music change\you start from the first turn, etc).