The overall desire to have children can go down within a society as things get either good or bad. The good part depends on having increasing amounts of resources (especially energy) so you don't need kids as farm slaves. The bad part depends on immiseration - decreasing resources and social cohesion - as happened in Russia as the Soviet Union crashed and burned.
Demographic transition works slowly and is very expensive in terms of resources used per birth avoided. Social crash is fast and cheap. In Russia the birth rate plunged by 50% in six years during the collapse. That's five times greater than the decline in industrialized nations over the same number of years.
As far as I'm concerned, there is no way to manage large-scale population change for planned outcomes. At least there's no way of doing that and maintaining the appearance of voluntary participation. My preference is simply to accept the situation, and watch it unfold - while acting as a witness to the demographic, ecological and cultural changes. If we allow things to unroll while always trying to understand What's Happening as clearly as possible, we have a greater chance of stumbling across a piece of knowledge that might prove useful.
I think hasty action based on insufficient information is a recipe for worsening the problem - as Dilworth points out that it always has been. My personal motto is "Don't just do something, sit there!" Think deeply before you act. Wait to see what new information comes up. Activists may take a dim view of this approach, but I'm convinced it will be healthier, safer, more certain and more virtuous in the end.