From families to nations, what binds individuals in social groups is the degree to which they share beliefs, norms, and memories. While local clusters of communicating individuals can sustain shared memories and norms, communities characterized by isolated cliques are susceptible to information fragmentation and polarization dynamics. We employ experimental manipulations in lab-created communities to investigate how the temporal dynamics of conversational interactions can shape the formation of collective memories. We show that when individuals that bridge cliques (i.e., weak ties) communicate early on in a series of networked interactions, the community reaches higher mnemonic convergence compared to when individuals first interact within cliques (i.e., strong ties). This, we find, is due to the tradeoffs between information diversity and accumulated overlap over time. By using data calibrated models, we extend these findings to a larger and more complex network structure. Our approach offers a framework to analyze and design interventions in communication networks that optimize shared remembering and diminish the likelihood of information bubbles and polarization.