Are Madonna-and-child images derived from pagan representations of goddesses?
Perhaps because there are women with children in every culture. Motherhood is a profound aspect of the human experience, and it should be expected to appear in a culture’s art and religion.
That two things are similar doesn’t mean one is derived from the other. After all, there are pyramids in Egypt and in Latin American, but no serious archaeologist believes one kind is derived from the other. The people in the two places simply made the same discovery: It is possible to build a stable building in the shape of a pyramid. In the same way, people in different cultures realized that motherhood is significant, and mother-and-child images became common in all cultures.
In the past one of the purposes of religious art was to instruct the illiterate. If you want to convey to someone who can’t read that a given painting is of Christ’s mother, how better to do it than by painting her with her infant Son?