Deep-diving sperm whales have a complex social structure and the largest brain of any animal, but very little is known about the ontogeny of their diving, foraging, echolocation, and communication skills. In large-brained terrestrial species, social skills develop earlier than locomotor abilities, but this may not be feasible for sperm whales, which require locomotor skills from birth to breathe, swim, and suckle. Here, we shed new light on the relative development of social and locomotor capabilities of a wild toothed whale. Sound and movement recording tags deployed on three first-year sperm whale calves for a total of 15 h revealed that these calves rarely produced codas for communication with adult whales, but likely tracked the ample passive acoustic cues emitted by clicking adults. The calves’ diving capabilities were well developed (maximum dive depth: 285, 337, and 662 m; maximum dive time: 11, 31, and 44 min) and they all produced clicks in a way that is consistent with echolocation. The calf performing the longest and deepest dives additionally emitted two echolocation buzzes, suggesting that it could have attempted to forage. Thus, sperm whale calves may supplement their milk diet with food caught independently at depth much earlier than previously believed. Contrary to terrestrial mammals, we propose that the maturation of locomotor, diving, and echolocation skills may be favored over investment in developing social communication skills at an early age in sperm whales.