The country of Georgia provides an example of how to reverse this problem - by embracing a pro-life religious values.
They raised their birth rate, and more importantly, did so with more 3rd and 4th children WITHOUT more illegitimacy.
Yes, Religious Influence Boosted Georgia’s Birth Rate
https://medium.com/migration-issues/yes-religious-influence-boosted-georgias-birth-rate-b5637b1d6858