The idea that White people generally have fewer offspring while not incorrect, is misunderstood. What causes this lower birth rate is the standard of living and general affluence of the population. The more affluent you are, the more likely you'll produce fewer offspring. Heck, out of 224 countries with the 224th having the lowest birth rate(Monaco) Japan is 222nd, Singapore 221st and South Korea is 220th. For those wondering what is 223rd, it's St. Pierre and Miquelon. Yeah, big shocker.
Oh, and for the few idiots that keep insisting Israel is committing genocide on Palestine, Palestine has the 35th highest birth rate on the planet while ethnic Palestinians are one
the fastest growing demographics on the planet, ranked at 25th IIRC.
If you look at the list of sovereign states by birth rate, you can see a general trend from the most affluent country to least although some of countries may seem skewed due to a variety of factors like their ethnic culture, immigration, etc. In many 3rd world countries the birth rates are high because in many instances, it's the only way of ensuring your genes survive to continue your line.
What's making a noticeable difference in population sizes is the drop in infant mortality rates in those countries, the fact they have been peopled for millennia and that it's only been recently (for them) that infant mortality rates have dropped so the inherent drive to reproduce as much as they can is still there.
https://en.wikipedia.org/wiki/List_of_sovereign_states_and_dependent_territories_by_birth_rate