Understanding the kinetics of shock-compressed SiO2 is of great importance for mitigating optical damage for high-intensity lasers and for understanding meteoroid impacts. Experimental work has placed some thermodynamic bounds on the formation of high-pressure phases of this material, but the formation kinetics and underlying microscopic mechanisms are yet to be elucidated. In this study, by employing multi-scale molecular dynamics studies of shock-compressed fused silica and quartz, we find that silica transforms into a poor glass former that subsequently exhibits ultrafast crystallization within a few nanoseconds. We also find that, as a result of the formation of such an intermediate disordered phase, the transition between silica polymorphs obeys a homogeneous reconstructive nucleation and grain growth model. We construct a quantitative model of nucleation and grain growth, and compare its predictions with high-pressure silica crystal grain sizes observed in laser-induced damage and meteoroid impact events. Moreover, we have studied the quantum nuclear effects for high-pressure silica crystallization. While quantum nuclear effects play important roles in shock-induced chemical reactions and phase transitions, they are absent in classical atomistic shock simulations. To address this shortcoming, we couple the shock simulation with a colored-noise Langevin thermostat. We find that this semiclassical approach gives shock temperatures as much as 7% higher than classical simulations near the onset of crystallization in silica. We have also studied the impact of this approach on the kinetics of crystallization and the position of high-pressure silica melt line.