I might be wrong but we called cradle roll, from the cradle or brought up in a SBC church from birth on.
Bob, you are right. When I was a child (about a century ago, it seems now), when a newborn was brought to church for the first time, he/she was enrolled in what was called the Cradle Roll Department. Once they were able to walk, (toddlers) they were promoted to the Nursery. The next step up is at four years of age, to the Beginner Department. Next was the Primary Department for seven and eights. At age nine, came the promotion to the Junior Department, and at age thirteen, to the Intermediate Department. That continued through junior high and high school (with various age-group classes), when they went to the Young People's Department, which was mainly college-age, and finally to the Adult Department.
Some of our oldest adults called their classes the Graveyard Department, where they stayed until they got the ultimate promotion--to Heaven.
The department names have changed somewhat over the years, mainly reflecting school divisions (such as Junior High, College and Career), but the principle of organizing age groups remains intact.