In Fallout 4, after the Sole Survivor's son is taken from the vault, they are refrozen in the cryogenic tube. After escaping from that, he or she goes on the quest to get their son back.
I haven't yet finished the game and maybe I didn't pay enough attention at the start, but to me it seems like the Sole Survivor is absolutely convinced Shaun is still alive and hasn't yet, well, died of old age.
When and how does s/he learn how much time has elapsed since the kidnapping? Do they know this from the start?