We're too close to matrix timeline for that. People will be pushed financially to sell their sperm and eggs to the government or a corporation for money so they can survive and that corporation will then grow a new generation of AI prompt givers.

We will also see things like further pushes against abortion, more lenient rape laws and other awful shit to pump up the births. There could also be importing births from other countries in the form of immigration. As we've seen with climate change, governments and corporations ultimately won't care about declining births regardless of how unsustainable it is.