Technological innovations have allowed humans to settle in habitats for which they are poorly suited biologically. However, our understanding of how humans produce complex technologies is limited. We used a computer-based experiment, involving humans and learning bots, to investigate how reasoning abilities, social learning mechanisms and population structure affect the production of virtual artefacts. We found that humans’ reasoning abilities play an important role in the production of innovations, but that groups of individuals are able to produce artefacts that are more complex than any isolated individual can produce during the same amount of time. We show that this group-level ability to produce complex innovations is maximized when social information is easy to acquire and when individuals are organized into large and partially connected populations. These results suggest that the transition to behavioural modernity could have been triggered by a change in ancestral between-group interaction patterns.