Fluent conversation requires temporal organization between conversational exchanges. By performing a systematic review and Bayesian multi-level meta-analysis, we map the trajectory of infants' turn-taking abilities over the course of early development (0 to 70 months). We synthesize the evidence from 26 studies (78 estimates from 429 unique infants, of which at least 152 are female) reporting response latencies in infant-adult dyadic interactions. The data were collected between 1975 and 2019, exclusively in North America and Europe. Infants took on average circa 1 s to respond, and the evidence of changes in response over time was inconclusive. Infants' response latencies are related to those of their adult conversational partners: an increase of 1 s in adult response latency (e.g., 400 to 1400 ms) would be related to an increase of over 1 s in infant response latency (from 600 to 1857 ms). These results highlight the dynamic reciprocity involved in the temporal organization of turn-taking. Based on these results, we provide recommendations for future avenues of enquiry: studies should analyze how turn-by-turn exchanges develop on a longitudinal timescale, with rich assessment of infants' linguistic and social development.