I have a concept for a story (see below) and a rough idea of what some of the characters will do to create the central plot point in it (again, see below), the issue is, I'm not sure what point in time, in real life history, it would be plausible for them to do those things. (Technically I'm not world building here but rather world choosing.)
A young couple (15-16 but able to look a bit older, or maybe up to early 20's if it makes the story work) choose to vanish on basically no notice. They have no prior planning for this and have to wing things until they figure stuff out. Eventually they establish new identities and are able to live a mostly normal life. They may need to avoid scrutiny but over time they build up enough real background to their assumed identities that they can do most everything that would draw attention to them if they didn't do it. (There may be things, e.g. working in sensitive jobs) they can't do, but by simply never trying, they is an issue that can go unnoticed.
Everything about what these characters do, beyond what I've already settled on and described above, is outside the scope of the question I'm asking. In fact, it's almost immaterial to the story because the story is a whydonit and will be from the perspective of the people who start out knowing only that the couple vanished and nothing that happened after that. That they do it is the only major plot relevant bit and I just need it to be not blatantly implausible.
Assuming this happens in the US (or some other currently first world nation), what is the approximate last point in time where it would be feasible for smart and motivated people to pull the above off with no prior planning or research? What happens at that point that makes it unreasonable?
There is a real world story of a WW-2 German POW in the US who didn't want to get repatriated to east Germany and so (after the war in Europe was over) escaped and succeeded at living a mostly normal life in the US for decades. That would suggest that c. 1944 would be not to recently.
On the other end, by the information age, it would seem that just showing up and saying you are "Johnathan Dow" would very quickly fall apart without significant skill and resources put into fabricating records in a lot of different places. That would suggest c 2000 would likely be to recently.
On the 3rd hand, even today there are a large number of people who have illegally immigrated to the US and have no identity they can use for most things. So depending on how much they need to do (I'm thinking my cases requires to much here), you may still be able to create a "good enough" assumed identity.
Edit: turns out at least some effort is being made to proactively seek out assumed identities without waiting for other indicators.