This is a myth that needs to die. People are already having less kids. Nearly the entirety of Europe is below replacement rate already, and all other industrialized or industrializing countries are following close behind. As poorer countries become less poor, with better access to contraception and education (for girls in particular), and lower child mortality rates, their birth rates are falling as well. China is projected to have a population of 1 billion in 2100, which is 400 million
fewer than today. Some projections have them as low as 7-800 million. India will also have hundreds of millions fewer people.
The only challenge is if global warming makes it so that the poor countries can't ever become not poor, but then what's the population growth solution? Invade them and force them to have fewer children?
Besides,
@Cheimoon is right, any change to population growth that happens
right now would take decades to have any effect. And all the kids in Africa are either way going to grow up and want to have children of their own. That ship sailed when those kids were born and survived early childhood.