Todd Howard specifically states that they were skipping to where he leaves the vault to avoid spoilers and just show off the game. It's not the very first thing that happens.

Indeed, however that doesn't resolve the fact that his first words on the outside are like "What year is it?" Rather than "Have you seen my family?" I mean if their home was right by the Vault it would be a logical place for them to be whilst asking his robot butler right?

I suspect that the PC notices that at-least the kid isn't in the Vault. What with child death not being a thing they aren't going to have the baby dead in the Vault are they?

It is a fair point that he doesn't ask about his family, but he could have been trying to find his family then escape from the vault for days.

They could have also cut that out for the presentation.

Or maybe his family didn't survive. Or maybe the Lone Survivor thinks they didn't.

And if they did some how leave the vault 20 years earlier, there is little to be done to find them at least right now.

I guess you would just hope you don't run across their bodies some where.

Well there's been child deaths. Nuke a town, destroy an inhabited vault. The assumption is there's kids there that will be killed. They just may not show the death.

But I believe it's pretty obvious the 'kid' will be back...

Even so that would be like "nuuuu !! where's mah family ?!" *walks a couple miles* "meh whatever, hungry now"

Also, if something like the 1st phrase is uttered my connection with the PC will die right there.