Ionizing radiation interactions in matter can trigger a cascade of processes that underpin long-lived damage in the medium. To date, however, a lack of suitable methodologies has precluded our ability to understand the role that material nanostructure plays in this cascade. Here, we use transient photoabsorption to track the lifetime of free electrons (τ_{c}) in bulk and nanostructured SiO_{2} (aerogel) irradiated by picosecond-scale (10^{-12} s) bursts of x rays and protons from a laser-driven accelerator. Optical streaking reveals a sharp increase in τ_{c} from <1 ps to >50 ps over a narrow average density (ρ_{av}) range spanning the expected phonon-fracton crossover in aerogels. Numerical modeling suggests that this discontinuity can be understood by a quenching of rapid, phonon-assisted recovery in irradiated nanostructured SiO_{2}. This is shown to lead to an extended period of enhanced energy density in the excited electron population. Overall, these results open a direct route to tracking how low-level processes in complex systems can underpin macroscopically observed phenomena and, importantly, the conditions that permit them to emerge.