Baby's Hair in the Womb. Babies start growing hair before they are even born, Kids Health says. By the 14th week of pregnancy, babies in the womb develop a layer of lanugo, which is a soft, fine hair that starts on his face and eventually covers his entire body. Hair starts to grow on a baby’s head as early as the 30th week of pregnancy and, by the 32nd week, the baby develops eyelashes and eyebrows.