Rain formation is a crucial element of weather and climate uncertainties and is a critical factor governing cloud lifecycle and forcing. But is it accurately represented in our atmospheric models? Turbulence is woven into cloud microphysical interactions at various scales, and thus is challenging to represent in atmospheric models with limited resolution capability. Several past experiments and numerical simulations postulated the impact of turbulence on rain formation through its influence on drop collision-coalescence. We provide direct evidence of the impact of turbulence on evolution of drop size distributions and rain drop formation by comparing high-resolution observations of cumulus congestus clouds with state-of-the-art large-eddy simulations coupled with a Lagrangian particle-based microphysics scheme. To our knowledge, this study evaluates the Lagrangian scheme against observations by comparing complete drop size distributions at different altitudes in cumulus clouds for the first time. It is shown that turbulent coagulation is necessary for accurately representing the observed drizzle range of drop size distributions at lower heights in cumulus congestus. Turbulence effects cause earlier rain formation and greater rain accumulation than using gravitational coagulation alone in the model. The observed rain size distribution tail just above cloud base follows a power law scaling but deviates from theoretical scalings considering either a purely gravitation collision kernel or a turbulent kernel without the droplet inertial effects. Large cloud condensation nuclei (“giant CCNs”) are also hypothesized by several studies to be of critical importance to drop size distribution evolution and rain formation. However, in this study, large aerosols do not significantly impact rain formation and drop size distributions. This is explained by the growth kinetic limitation of large aerosols; the time for these particles to reach equilibrium is longer than the lifetime of rising cumulus thermals, so they generally do not activate as cloud drops. Overall, it is concluded that the turbulent coagulation of drops exerts a dominant influence on rain initiation in warm cumulus congestus, with limited impact of giant CCN.