Firms in the developing world exhibit much flatter life-cycle dynamics compared to firms in developed countries. This paper examines the role of demand constraints in limiting the growth of small and medium firms in Brazil. We test whether firms that win government procurement contracts grow more compared to firms that compete for these contracts but do not win. We assemble a comprehensive data set combining matched employer-employee data for the universe of formal firms in Brazil with the universe of federal government procurement contracts. Exploiting a quasi-experimental design, we find that winning at least one contract in a given quarter increases firm growth by 2.2 percentage points over that quarter, with 93% of the new hires coming from either unemployment or the informal sector. These effects also persist well beyond the length of the contracts. Part of this persistence comes from firms participating and wining more future auctions, as well as penetrating other markets.