I agree the whole thing could have fizzled out in the 50s, but the Nazis were hoping for a massive growth rate increase and, at high levels, they seemed to genuinely want Germans to settle the east. It is a core part of Nazi doctrine (
Volk ohne Raum, people without space) that Germany had too many people crammed into too little space. (They would have marveled at the level of density in democratic Germany today... practically all the land is developed in some way.) I think that, no matter what the outcome of Generalplan Ost, there would be an influx of people into the annexed areas of the Reich, that is, the areas lost after 1918. That could happen with the same level of population growth.
But, again, that's not what top-level Nazis wanted. There is a set of wall posters about population and the urban/rural divide
here. For a more in-depth discussion on space and birth rates see
here. One slide shows the average family size in 1870-1900 compared to 1900-1930. The author clearly views the 1870-1900 condition as preferable, and the ideal in the poster is a farm family with eight children. Overall, eight children is roughly what the Nazis wanted a good German family to have: four as a bare minimum (200% growth per generation), six as average (300% growth) and eight or more as ideal (400+% growth).
The question is, then, how the Nazi government was going to facilitate that high birth rate. Plans were underway, with the sanctification of large families via the Cross of the German Mother, and undoubtedly many Reichsmarks would have been spent post-war on benefits for large families. I don't think the Nazis would have forced people to have large families, via things like banning contraception; they would have encouraged having eight children as the summit of achievement for a German woman, and they would have believed that woman's daughters would be selected (by social Darwinism) to be good child-bearers in turn. Women who didn't want to have children weren't the sort of women Hitler was looking for.
What I mean by all this is that a leap in birth rates is entirely plausible. Ultimately the plan would succeed or fail by the willingness of German women to bear the appropriate number of children, but with some encouragement it's possible to see a return to 1870-1900 family sizes. What this means for Generalplan Ost is that there's a good chance the necessary people would be available in the 50s and 60s. Many of the post-war generation would choose to stay in the old Reich, but some would have to move to the East.
Earlier I said that Eastern Front soldiers might be the first in line to settle; I think that was well refuted. One eager category, perhaps, would be the well-indoctrinated children born in 1933 or later, children who had never known anything except the Nazi state, and who would be unfailingly loyal to it. (They'd be loyal to the state before their parents, in Orwellian fashion.) In other words, when a boy at a Hitler Youth camp got a little too close to a similarly aged girl in the BdM -- which happened all the time -- then it would be accepted without question that they should start a family in the East.