Just watched the trailer again, particularly paying attention to all of the pre-war elements, and I have a few ideas/theories as to how we may begin our journey in the next Fallout instalment. Apologies if any of the following has already been covered:
1. The inclusion of so much pre-war content suggests that we would almost certainly begin in this era, most likely on the day of the great war - namely October 23rd 2077. It is highly unlikely that this much content would have been created just for the trailer. If this is the case, then the initial character creation process would also likely be during the initial pre-war section.
2. There is an undeniable likeness between the guy we first see in the house (with the wife and child) and then standing above the vault, and the protagonist at the end of the trailer, which would suggest that they are in fact the same person. This would also tie in with previous info suggesting cryogenics as being the predominant feature of vault 111. The fact that they are standing on what looks like a lift leading down into the vault would allow a way for the protagonist's family to be "rescued".
3. Evidence suggests that we should be able to play as either a male or female protagonist as per previous fallout titles, which could well mean that we will end up playing either one of the parents features in the trailer. My personal theory is that we initially choose which parent we would like to play as, and upon entering the vault, only that parent survives, along with the child. The other parent would perhaps be too badly affected by radiation to survive, and then you and your child are put into cryosleep as part of the vault protocol, most likely against your wishes.
4. If the cryogenics theory is correct, then we could end up with a situation where you and your child awaken at different times, possibly even years apart. For example, somebody (either a group or an individual) enters vault 111 many years after the great war and discovers the first cryochamber containing your child and they revive them. They then take the child. Several years later, your own cryosleep is disrupted (possibly by the dog in the trailer?) and you also awaken. You discover that your child (who could now be many years older) is gone. You then have an incentive to find them, hence opening up the story line. This could allow for any number of possibilities, such as your child being raised/indoctrinated by a questionable organisation and you perhaps later confronting them as some kind of nemesis.
5. The character creation component could actually be based around the child (at a later age, similar to F3) which could then perhaps determine the physical appearance of both parents. You would then, in theory, be able to choose which of the parents you choose to play as - maybe even having to decide which parent is saved upon entering the vault, who would then become the protagonist.
Again, this is all just theory at this stage, but it will be interesting to see how this pans out in the final release. Whatever happens, I'm sure we are all in for a real treat. I for one will be spending many many hours exploring the new wasteland when the time comes...
Edit: after much discussion/reflection, I would be more inclined to believe an only survivor scenario would be more realistic. This would still tie in with the other elements of my theory, but would allow much more player freedom without being tied down too much to the past. This would also be more in line with Bethesda's philosophy of letting the player tailor their own experience.