A country does not become industrialized by people starting to have kids at a later age.
There is a theory that supports this:
A core mechanism of unified growth theory is that accelerating technological progress induces mass education and, through interaction with child quantity-quality substitution, a decline in fertility.
Declines in fertility have been observed after a country has become industrialized. Not only did fertility decline, but the children people were having were generally 'of higher quality'.
The testable predictions of the theory and its underlying mechanisms have been confirmed in empirical and quantitative research in the past decade, and have inspired intensive exploration of the impact of historical and pre-historical forces on comparative economic development and the disparity in the wealth of nations.
There is a theory that supports this:
Declines in fertility have been observed after a country has become industrialized. Not only did fertility decline, but the children people were having were generally 'of higher quality'.
https://onlinelibrary.wiley.com/doi/full/10.3982/QE1751
This comes from Wiki, and this particular statement currently has 3 citations if anyone is interested: https://en.wikipedia.org/wiki/Unified_growth_theory