Silica glass is a high-performance material used in many applications such as lenses, glassware, and fibers. However, modern additive manufacturing of micro-scale silica glass structures requires sintering of 3D-printed silica-nanoparticle-loaded composites at similar to 1200 degrees C, which causes substantial structural shrinkage and limits the choice of substrate materials. Here, 3D printing of solid silica glass with sub-micrometer resolution is demonstrated without the need of a sintering step. This is achieved by locally crosslinking hydrogen silsesquioxane to silica glass using nonlinear absorption of sub-picosecond laser pulses. The as-printed glass is optically transparent but shows a high ratio of 4-membered silicon-oxygen rings and photoluminescence. Optional annealing at 900 degrees C makes the glass indistinguishable from fused silica. The utility of the approach is demonstrated by 3D printing an optical microtoroid resonator, a luminescence source, and a suspended plate on an optical-fiber tip. This approach enables promising applications in fields such as photonics, medicine, and quantum-optics.