The pre-Christian Roman Empire was rife with homosexuality, beastiality, pedophilia, abortion, and infanticide by exposure.
They did not value children much.
Jews and Christians saw children as a gift from G-d. They valued them immensely. In the Old Testament, G-d is adamant about child sacrifice, calling it an abomination.
Christians and Jews simply had more children, took better care of them, and often adopted children pagan Romans abandoned to die by exposure.
There were other factors of course.
Moses mother hid him in the bulrushes.