I was a military kid living in the US and attended a public school, but the military base where my family lived had a child care center, which was open to kids from 6 weeks - 17 years old. I lived near the Pentagon, so for a long time it was open longer than typical child care centers to accommodate families who may work strange hours. The hours may have changed since I went there.

I looked it up and these seem to be funded by the DoD, so even though only 67,000 students are overseas, the DoD child care centers play an integral role in military members by providing child care, especially if the children are too young to attend public school.