There are so many theories going around, and a lot of them have great points, but also have faults in them. One basic one is that you and/or your family are actually androids and possibly this vault is an android vault. This could be an alternative to the massive cryogenic theory. Now the only problem that i can see with this is the fact that your baby would be an android. to me, it just wouldn't make sense for their to be an android baby in the fallout universe. They have the tech. to make unbelievable androids, why waste it to make a baby.
The other huge theory is that you are in a cryogenic sleep. This is the most popular and most probable theory to the beginning of the story, however has some questions to answer. If you find your pip-boy on a dead scientist, why would he have died. As a scientist, he would most likely be watching over the machines to make sure nothing happened, so food, water and other necessities were most likely given. this would leave an attack of some sort. In this case however, cryogenics would most likely be broken. Lets be honest a weapon could somehow break or disarm these machines. If this happened, the Lone Survivor would've had an encounter already, or would be killed.
Another thing to think about is how the vault actually opens. I could be wrong but it looked as if the door opens horizontally, since they are standing on top of the vault when nuke goes off. In other games the door was vertical, like any other door in life would be. Although one thing i noticed is when you actually get the pip-boy, there is a vertical facing door.This brings into question how everyone gets into the vault after the giant wind bursts from the nuke hit you. It would seem the platform lowers, so would people be blown away, including the family?
The beauty of theories is it is all speculation. In my opinion, the platform to the vault lowers/you get in somehow, and the PC gets in without his family and at least some other people afterwards. Since the nuke went off before everyone could get safely inside, the scientist and several people medical patch everyone up quickly, and everything is in sort of a panic. I think then you are placed in a cryogenic sleep. I still don't have a great guess at if you are aware you were going to be put there, or were so drugged up from the blast and they just put you in quick. I do believe your kid is alive, with your significant other a possibility to live. It's much easier to kill off the advlt and have it be emotional than the kid. I'm still very confused about how you are the only one surviving but i'm going to say that everyone else in the vault had to severe of injuries and died right away, and maybe a couple opened early. whether on purpose or accident i'm not sure. those people would've probably left. I think you then leave the vault to find out what happened to your family and that is the main quest. Along the main quest, you will probably deal with the fights between BoS and other rebel groups such as the androids from the Institute.
Please criticize or point out any flaws/more ideas. This is just a rough guess.
I'm from Mass. so this game feels so much cooler for me than for other people i feel like.