We investigate the evolution of the electronic structure of fused silica in a dense plasma regime using time-resolved x-ray absorption spectroscopy. We use a nanosecond (ns) laser beam to generate a strong uniform shock wave in the sample and a picosecond (ps) pulse to produce a broadband x-ray source near the Si K edge. By varying the delay between the two laser beams and the intensity of the ns beam, we explore a large thermodynamical domain with densities varying from 1 to 5 g/cm^{3} and temperatures up to 5 eV. In contrast to normal conditions where silica is a well-known insulator with a wide band gap of 8.9 eV, we find that shocked silica exhibits a pseudogap as a semimetal throughout this thermodynamical domain. This is in quantitative agreement with density functional theory predictions performed using the generalized gradient approximation.