In a gameplay vid, the male PC speaks to Codsworth as though he'd just went into the vault, which suggests that our player character has been uncounscious in some sort of cryostasis state within the vault.
Way I see it, Vault 111 releases it's cryogenized inhabitants one at a time at set intervals of years. Player character happened to be the last one exactly 200 years after the apocalypse.
Our son will have been released alongside the NPC mother/father decades before the player, and we will meet him as an advlt. His appearance will be generated based on the mother and father we created [I believe Todd said as much in the gameplay vid].
It feels like a rather obvious thing to do if they're gonna bother giving the player a set backstory with a family. It feels pointless to introduce the family with all these gimmicks and then kill them off 5 min into the game.
We're gonna be seeing way more of that family, or at the very least, of Shaun. They did say they wanted to do a dramatic story this time around, having a grown up Shaun going about seems somewhat dramatic.