Social cognition in infancy is evident in coordinated triadic engagements, that is, infants attending jointly with social partners and objects. Current evolutionary theories of primate social cognition tend to highlight species differences in cognition based on human-unique cooperative motives. We consider a developmental model in which engagement experiences produce differential outcomes. We conducted a 10-year-long study in which two groups of laboratory-raised chimpanzee infants were given quantifiably different engagement experiences. Joint attention, cooperativeness, affect, and different levels of cognition were measured in 5- to 12-month-old chimpanzees, and compared to outcomes derived from a normative human database. We found that joint attention skills significantly improved across development for all infants, but by 12 months, the humans significantly surpassed the chimpanzees. We found that cooperativeness was stable in the humans, but by 12 months, the chimpanzee group given enriched engagement experiences significantly surpassed the humans. Past engagement experiences and concurrent affect were significant unique predictors of both joint attention and cooperativeness in 5- to 12-month-old chimpanzees. When engagement experiences and concurrent affect were statistically controlled, joint attention and cooperation were not associated. We explain differential social cognition outcomes in terms of the significant influences of previous engagement experiences and affect, in addition to cognition. Our study highlights developmental processes that underpin the emergence of social cognition in support of evolutionary continuity.