We have performed replica-exchange reaction ensemble Monte Carlo simulations to study the low-energy crystalline structures of a reactive model of silica. We have utilized a model of silica polymerization based on the reactive assembly of semiflexible tetrahedral units developed by us previously to reproduce silica bulk moduli as well as self-assembly of amorphous silica gels and nanoparticles. Our implementation of replica-exchange Monte Carlo involves simulating several system copies, each with its own value of the equilibrium constant controlling silica condensation/hydrolysis reactions, which are essential for building higher-order network structures and eventually crystals. These replica-exchange simulations were found to traverse energy landscapes from amorphous to crystalline phases, yielding the dense silica polymorphs α-cristobalite, β-cristobalite, and keatite, as well as the nanoporous silica materials SOD and EDI and nanoporous phosphates with DFT and ATT structures. Simulated crystal structures were confirmed by computing X-ray patterns for comparison with known XRD data. The behavior of this model opens the door to future simulation studies of the free energy barriers controlling these crystallization processes.