How did 子, meaning "child", become a noun suffix? It's really impressive how 子 [zi] is super productive as a noun suffix. But I can't see any relation of how the idea of "child" could turn into a suffix.

Thanks!
It's called a diminutive suffix, about which you can read these entries:

https://en.m.wikipedia.org/wiki/Diminutive

https://en.m.wikipedia.org/wiki/List_of_diminutives_by_language