The only real question I have at the end of Fallout 4, is if they left it purposefully open that you could be a Synth.
You were woken up by Kellogg, who took your Baby, and then you run into Kellogg again 60 years later, after the cryo facility shuts down, with only you alive. When you are going through Kelloggs memories, he talks about "The Old Man" the leader of the institute, as if it's the same guy the whole time. That means either Kellogg doesn't know that the Insititute changed Leaders while he was active, or Kellogg has had his memories altered somehow, and instead of being re-frozen., your DNA was taken from your dead body in the cryo facility and used to make a Synth duplicate which was then placed there. And for some reason a perfectly functional vault and Sanctuary has been relatively abandoned for hundreds of years.
I don't know if it's bad writing, or if that the writers intent was to suspect you were a Synth, since some things don't add up. Like making a Synth of your son for no good reason, since he would never age and yet, if you were a normal human you would age and die before his eyes. So I wonder if the plan was to make you as a covert Synth take over the institute.
Other people point out VATS is also available before you put on the Pip-Boy. Which people say is just a bug, but the game is still based on the same Gamebryo engine that never allowed VATS before the Pip-Boy was obtained.
And remember at the start of the game, you cannot leave the house until you have Shaun, he is always within earshot of anything taking place before you wake up. So it could mean the start of the game aren't your memories, but Shauns memories, placed there.