This is completely backward. Many First World countries plus Russia and Eastern European nation are already procreating at or below replacement levels, while many Third World countries have high levels of population growth. Further depopulation of First World countries is entirely the wrong advice. They need to have higher fertility rates to support their existing societies. If we want our culture and society to survive, we need to foster population growth at the same level as thd world average.
It is almost a tautology to say the countries with the highest rates of population growth are the most responsible for increases in the global population. Similarly, the countries with increasing rates of CO2 emission are most responsible for increases in the worldwide emission of CO2. China, India, Bangladesh, and many Third World nations have planned to increase the number of coal fired power plants. The US has reduced its coal consumption and its CO2 production. The real focus should be on stopping 3rd World increases in CO2 emissions.
The large rate of population growth in the Third World exacerbates existing poverty there and is leading to large scale immigration. A policy of curtailing immigration from countries with high rates of reproduction and/or high rates of growth in CO2 emissions will force them to deal with the crisis of overpopulation and excessive CO2 production.