We explore how connections between buyers and suppliers of intermediate inputs evolve over time to promote firm growth. To formalize this process we develop a dynamic model of a granular endogenous production network, making stark assumptions that yield a tractable parsimonious framework. In the model, producers gradually build up a network of contacts by meeting other producers and source an intermediate input from their cheapest contact at any moment. They retain full recall, so can always switch to a producer contacted previously, even if they never bought from it before. Through this process the production network itself becomes an endogenous state variable in the model that drives firm growth. Despite its simplicity, the implications we derive from this framework are realistic enough to test against numerous findings from the burgeoning empirical literature on firm-to-firm trade.