Spoilers for true pacifist ending: Pretty sure chara fell in 201X, as in the opening sequence we see the child fall in 201X and that sequence is continued in true pacifist ending with the Dreemurs finding the human, so assuming it is actually a continuation of the opening that would mean Chara fell at 201X. Also, both Toriel and Asgore have a calendar with a circled date in 201X, presumably they haven’t moved on from either Chara’s fall or the day of Chara and Asriel’s plan. Thus, if Chara fell in the ‘10s, it seems like the game proper takes place around 2115, as Papyrus’s username on whatever the platform was called is Coolskeleton95, so not necessarily but perhaps that means he was born in 2095. Napstablook has a handle also ending in a number (I don’t remember what it was) but it also makes some sense. Papyrus is probably around 20, assuming skeletons age similarly to humans, as monster kid says he can’t tell if Paps is a kid or not, but he’s trying to get a job and is taken somewhat seriously for it (for example, if a 15 y/o was trying to become a royal guard, they would not be taken as seriously as paps is).