The crystallization dynamics of a colloidal cluster is modeled using a low-dimensional Smoluchowski equation. Diffusion mapping shows that two order parameters are required to describe the dynamics. Using order parameters as metrics for condensation and crystallinity, free energy, and diffusivity landscapes are extracted from Brownian dynamics simulations using Bayesian inference. Free energy landscapes are validated against Monte Carlo simulations, and mean first-passage times are validated against dynamic simulations. The resulting model enables a low-dimensional description of colloidal crystallization dynamics.