The preparation of two-dimensional covalent organic frameworks (2D COFs) with large crystalline domains and controlled morphology is necessary for realizing the full potential of their atomically precise structures and uniform, tailorable porosity. Currently 2D COF syntheses are developed empirically, and most materials are isolated as insoluble and unprocessable powders with typical crystalline domain sizes smaller than 50 nm. Little is known about their nucleation and growth processes, which involve a combination of covalent bond formation, degenerate exchange, and non-covalent stacking processes. A deeper understanding of the chemical processes that lead to COF polymerization and crystallization is key to achieving improved materials quality and control. Here, we report a kinetic Monte Carlo (KMC) model that describes the formation of a prototypical boronate-ester linked 2D COF known as COF-5 from its 2,3,6,7,10,11-hexahydroxytriphenylene and 1,4-phenylene bis(boronic acid) monomers in solution. The key rate parameters for the KMC model were derived from experimental measurements when possible and complemented with reaction pathway analyses, molecular dynamics simulations, and binding free-energy calculations. The essential features of experimentally measured COF-5 growth kinetics are reproduced well by the KMC simulations. In particular, the simulations successfully captured a nucleation process followed by a subsequent growth process. The nucleating species are found to be multi-layer structures that form through multiple pathways. During the growth of COF-5, extensions in the lateral (in-plane) and vertical (stacking) directions are both seen to be linear with respect to time and are dominated by monomer addition and oligomer association, respectively. Finally, we show that the experimental observations of increased average crystallite size with the addition of water are modeled accurately by the simulations. These results will inform the rational development of 2D COF polymerizations to control the rate of nucleation, thereby increasing their materials quality.