Yeah I wouldn't be all that surprised if Vault 111 was the birth place, or at least connected to, the origin of synths in general. Scientists and egg heads from MIT and other places hid in their vaults and spend however long they were down there testing and experimenting with artificial life, and you are one such attempt. Either a hybrid Human/android or just a pure android that utilized a human donors memories to function. Right now I'm guessing it's the latter, but either work if you were outside the vault when the nuke went off in the trailer. No way you just get hit with that explosion and go into a vault all fine and dandy. You'd be irradiated and totally fucked up. After that kind of exposure and blast you'd be luck to be a brain in a jar.
So then 200 years later either you got mothballed and wake up on chance, or you are woken up on purpose and led to believe you're a real human. They couldn't directly access your memories so the hope is that if you are left to figure things out on your own, try and find your wife and child, you'll remember those latent memories on whatever it is they want. Meanwhile your wife and child are long dead themselves.
Thinking about this I'm basically describing Terminator Salvation.