Here's my theory on the story of Fallout 4. This is gonna be a short on. My guess is The Sole-Survivor finds his kid, however, he'll be an old man, or at least, older than. Or perhaps even be dead, for a few decades, and decides to look for his son's kids. Also, Vault 111's experiment is most like Cryosuspension, but my guess is the experiment was to release on person every year or so. This would explain the kid being older or dead.