Protein assembly is a main route to generating complexity in living systems. Revealing the relevant molecular details is challenging because of the intrinsic heterogeneity of species ranging from few to hundreds of molecules. Here, we use mass photometry to quantify and monitor the full range of actin oligomers during polymerization with single-molecule sensitivity. We find that traditional nucleation-based models cannot account for the observed distributions of actin oligomers. Instead, the key step of filament formation is a slow transition between distinct states of an actin filament mediated by cation exchange or ATP hydrolysis. The resulting model reproduces important aspects of actin polymerization, such as the critical concentration for filament formation and bulk growth behavior. Our results revise the mechanism of actin nucleation, shed light on the role and function of actin-associated proteins, and introduce a general and quantitative means to studying protein assembly at the molecular level.