Regarding "religion": do you think "religions" came up with the concept of having a lot of children?
You don't think it's simply a natural instinct, like in all other animals? And that in a world where few make it to adulthood, people tried to have more children?
It's pretty well-established that it isn't poverty per se but gender equality that predicts birth rates.
Here is a blog post of the author in case the above is not readable for you: https://www.niussp.org/article/gender-equality-and-fertility...
This study is in the context of previous assumptions of a U-curved relationship: low equality == high birth rates, medium equality == low birth rates, high equality == high birth rates. That study shows that the last part doesn't seem to be true.
The macro trend of poverty <> birth rates points in the opposite direction: https://en.wikipedia.org/wiki/Income_and_fertility
Data points on the very poor end are all over the place, though.
The high workforce participation -> low birth rate correlation is definitely visible over time: https://ourworldindata.org/grapher/fertility-and-female-labo...