I think there's so much ill-founded assumptions in eugenics BS that it's hard to know where to start, but as a genealogist, I can personally verify that upper or middle class, wealthier people, presumably the sort eugenicists identify with, clearly had at least a 2-3 generations head start on the demographic transition where I come from.

There are other trends, there's always some groups of people who started having fewer kids earlier or later for reasons not obviously related to class - but class is the big one.