I have heard that the origins of the mother and child image in worship started in ancient Babylon. Was there a worship of a mother and child image in ancient Babylon of a prominence that we can conclude that it spread to other places? Thank you.
Yes and no. "Madonna" always refers to the Virgin Mary. However, yes, there is art for mother and child in Babylonian art, as well as art from pretty much every ancient civilization. Birth and fertility have always been a huge part of civilization, and for good reason. When people commonly die in their 20's, 30's if they're lucky, keeping the population up is a necessity. So they would make statues and pray to gods and do rituals so that they may bare children.
What matters here is context. In ancient societies, mother/child art was a way of prayer for fertility. In Christianity, it is a celebration of the birth of the Messiah from a virgin. It is not a prayer to bare children and keep society going, but rather a celebration.
You also have to remember that Christianity was illegal for quite some time, so creating art celebrating it was punishable. This is why we don't see many artifacts from early Christian society the way we do with ancient society.