All trends show that the countries with low levels of poverty, high levels of education and women equality results in fewer births.
Women are able to have careers and want to finish their education and get work experience before they think of children. In countries like Scandinavia, the average age of first time mothers are increasing year by year. We also see that cities within the country with a lot of highly educated jobs have a higher age than others
The anti-natalism movement has it right IMHO. If we voluntarily limit birth to far less than replacement, overpopulation would correct itself in as little as a generation. But we won't do that, we're not wired that way. Instead, we'll keep chugging along past the carrying capacity of the biosphere and Gaia will correct our population for us, abruptly.
That's also an argument against your point about war, disease, and famine.
Education of women is linked to a more K-Stategy approach among many other reasons on a personal level (ambitions to a higher purpose, learning in detail all of the cringe inducing ways an already known to be painful birth can go wrong for you and your children). K-strategy is all about quality over quantity which is what we actually want and need anyway. While a largely uneducated nation may say export the most logs with a large uneducated populace with handtools as lumberjacks - what they need from the transaction is money and lumber is better. And from there to furniture and a more advanced industrial economy.
Impactful funds you can support: https://impactful.ninja/best-charities-for-female-education/