Glasses can be produced via several routes, e.g., melt-quenching, sol-gel, irradiation, or vapor deposition. However, it remains unclear to what extent the structure, thermodynamical stability, and properties of glasses depend on the method of synthesis. Here, based on reactive molecular dynamics simulations of glassy silica samples, we investigate the network topology and thermodynamics of glasses prepared by melt-quenching, sol-gel, irradiation, and vapor deposition. We show that, depending on the synthesis route, silica glasses can exhibit an allowable or forbidden structure, that is, which is accessible or not by melt-quenching. These results pave the way toward the development of new “forbidden” glasses with exotic structure and properties.