Affiliative social bonds are linked to fitness components in many social mammals. However, despite their importance, little is known about how the tendency to form social bonds develops in young animals, or if the timing of development is heritable and thus can evolve. Using four decades of longitudinal observational data from a wild baboon population, we assessed the environmental determinants of an important social developmental milestone in baboons—the age at which a young animal first grooms a conspecific—and we assessed how the rates at which offspring groom their mothers develops during the juvenile period. We found that grooming development differs between the sexes: female infants groom at an earlier age and reach equal rates of grooming with their mother earlier than males. We also found that age at first grooming for both sexes is weakly heritable ( h ² = 0.043, 95% CI: 0.002–0.110). These results show that sex differences in grooming emerge at a young age; that strong, equitable social relationships between mothers and daughters begin very early in life; and that age at first grooming is heritable and therefore can be shaped by natural selection.