The elimination of poverty requires universal provision of education, women get educated, have less (no kids), birth rate drops and keeps dropping below the threshold of population stability.
I don't think there is any example of a society that has managed to reverse this trend. Maybe Ceaucescu Romania which at one point banned contraception and abortion, leading of course to the orphan crisis of the 1980's. Counter intuitively, devastating wars / famine also lead to post-crisis population boom, perhaps because education / career are entirely disrupted.
We probably need to think seriously about making people outside of the natural womb, can't see another way to reverse this trend outside of the above mentioned measures / circumstances