Lots of things happening with the intro. However, it's bits and pieces. We have the protagonist at the end, father/mother/child outside of the vault and the Vanishing Man. I think the trailer is shown with a default place holder. I believe we will either be the father or the mother by choice.
The Vanishing Man places the potential PC at the vault on the day of the war in a vault suit. This could be results through tech offered in the Memory Den. We know this tech can be directly related if not exclusive to Androids. However, I don't think we can rule out the possibility human application.
111 is highly thought to contain upper echelon officials. Given the area of the Commonwealth, it could be suggested that it was populated scientists and engineers.
Human mimicking wasn't fully developed until after the war. Pre war, the PC could be at a groundbreaking threshold of advancing android technology. Thus, making them a valued asset to recover if lost.
The PC and their immediate family arrive moments too late and perish in the blast. I think it would be too "cliffhanger common" to have the surface hatch activate to rescue them and have the blast blow over their heads as they decent.
Pre war, we do not have cryo advanced enough to sustain prolonged suspension beyond a decade or two. It is possible that they will write in some experimental tech that went as planned or malfunctioned into a new discovery but there isn't enough historical support for it to be utilized. Not impossible but you're at the mercy of the writer to make sense of it.
If the PC is an android, which I feel more plausible than cryo, it would explain the Vanishing Man, Memory Den and the flashbacks and the deaths. The Vanishing Man was an advanced AI that witnessed the peril, only at that time he may have simply been the AI implemented in their personal Mr. Handy, as a sign of Dr.X bringing their work home. This could be the result of disgruntled colleagues or their ideas were no longer supported by the Commonwealth suits, as an effective avenue of research. This theory supports the notion of Dr. X being shut out of 111 and your trusty Mr. Handy sees it all.
Holotapes with details of DR. X's research were recovered by Dr. E, that seeks to continue the work. Further investigations reveal Dr.X was actually able to upload his conscious into an AI and house it inside a home robot. This file remained dormant and parts of it was discovered wile and old tinkerer was scraping up parts. This AI was obviously different but it suffered form corrupt files that blocked it's memory.
The AI falls into the hands of Dr. E and the research continues. Dr E finally gains access to some of the files and accidentally initiates the conscious program of Dr. X. Confused and utterly terrified Dr E explains what happened. DR X is now a sentient AI in a desolate wasteland of the future.
Advanced android technology allows DR. E to fabricate an exact likeness of DR. X from pictures within Commonwealth archives. The PC, Dr. X now sets out to recall the details of that day with memories through the eyes of a robotic household assistant.