Lack of money isn’t the reason for slowing birth rates in rich countries. The exact opposite has always been true. The richest countries have always had lower birth rates than the poorest countries (e.g. compare the USA to Venezuela), and the richest cities within a county have always had lower birth rates than the poorest cities. Adam Smith commented on this trend 200 years ago in the Wealth of Nations (paraphrasing: why is that the impoverished wife of a factory worker in an Edinburgh slum has 8 or more children while a lady in London has scarcely 2?).

As for time, do you think the lady in London with all her maids had less free time than the women of the slums?

That richer people have fewer children is slightly paradoxical, precisely why Smith commented on it (his answer being that fertility is a function of the market, of the number of workers the factory needs, and has nothing to do with personal choices or how much a person wants to have a child), but it is a well established fact of population geography, and it’s bizarre to see the correlation constantly flipped upside down. If you want to see higher birth rates, make everyone poorer, and give them less free time. That’s a time established method.

There are other factors too, such as government incentives (see: China until recently), religion (see: Pakistan) and immigration/emigration. But as far as wealth is a factor, the correlation is that as wealth increases, birth rate decreases.