The goal of this work is to model the heterogeneous recombination of atomic oxygen on silica surfaces, which is of interest for accurately predicting the heating on vehicles traveling at hypersonic velocities. This is accomplished by creating a finite rate catalytic model, which describes recombination from an atomistic perspective with a set of elementary gas-surface reactions. Fundamental to surface catalytic reactions are the chemical structures on the surface where recombination can occur. Using molecular dynamics simulations with the ReaxFF potential, we find that the chemical sites active in oxygen atom recombination on silica surfaces consist of a small number of specific defects. The individual reactions in our finite rate catalytic model are based on the possible outcomes of oxygen interaction with these defects. The parameters of the functional forms of the rates, including activation energies and pre-exponential factors, are found by carrying out molecular dynamics simulations of individual events. We find that the recombination coefficients predicted by the finite rate catalytic model display an exponential dependence with temperature, in qualitative agreement with experiment at between 1000 K-1500 K. However, the ReaxFF potential requires reparametrization with new quantum chemical calculations specific to the reaction pathways presented in this work.