Population booms in good times hence the boomers during the post-war economic expansion. It isn’t a Children of Men scenario. Parenting is one of if not the biggest economic decision people face in their lives.
No single issue like free child care will change things. Unless we see real wage growth again and better affordability of housing and utilities we won’t see higher birth rates. It is a huge sacrifice for many people and turns very stressful in a bad economy.
It’s not even only for the parents themselves. One of my brothers has a kid and he and my sister-in-law are worrying all the time whether my niece will have a good chance at life at all… And their decision to get 1 child was well planned and they are well off and still they worry a lot. Even considering leaving Germany.