The two most crucial focuses would be to decarbonize carbon intensive economies, and throwing massive amounts of money at education and healthcare for women in developing countries.
Developed countries already have total fertility rates at or below replacement rate; it's all population momentum now, so you want to reduce the impact of everyone living a first world life for the remainder of their life span. Less combustion vehicles, less unnecessary air travel, fossil generation plants, meat heavy diets, etc. We're already headed in this direction, we just need to invest more heavily (Green New Deal, ESG funds, etc).
Regarding education and healthcare in developing countries, educated, empowered women with access to robust healthcare have fewer children [1] [2], and this data holds true across the entire world, even in countries that attempt to use generous subsidies to encourage higher fertility rates.
Moving folks from the developing world to the developed world, or vice versa, wouldn't have a meaningful impact IMHO.
[1] https://ourworldindata.org/fertility-rate#empowerment-of-wom...
[2] https://ourworldindata.org/grapher/womens-educational-attain...