We determine the thermodynamic phase diagram of the epitaxial SrTiO3/Si heterostructure from first principles density functional theory calculations. We demonstrate that the system is not thermodynamically stable with respect to formation of an interfacial SiO2 region under any experimentally attainable oxygen partial pressures. To understand the experimental observation of an atomically abrupt interface without an SiO2 layer, we construct a kinetic model of the growth process. We show that the observed stability of the non-equilibrium interface under both growth and ambient conditions is directly related to the interface chemistry, which gives rise to a large (2.2 eV) barrier for oxygen diffusion to the interface layer and kinetically traps an atomically abrupt interface structure. Our model leads to the prediction of an interface structure in good agreement with experiment, demonstrating that a combination of first-principles computations, thermodynamics, and simple kinetic modeling can be used to determine non-thermodynamic equilibrium atomic structures in complex heterosystems.