Motivated by the need to study nonequilibrium evolutions of many-electron systems at the atomistic ab initio level, as they occur in modern devices and applications, we developed a quantum dynamics approach bridging master equations and surface hopping (SH). The Lindblad master equation (LME) allows us to propagate efficiently ensembles of particles, while SH provides nonperturbative evaluation of transition rates that evolve in time and depend explicitly on nuclear geometry. We implemented the LME-SH technique within real-time time-dependent density functional theory using global flux SH, and we demonstrated its efficiency and utility by modeling metallic films, in which charge-phonon dynamics was studied experimentally and showed an unexpectedly strong dependence on adhesion layers. The LME-SH approach provides a general framework for modeling efficiently quantum dynamics in a broad range of complex many-electron condensed-matter and nanoscale systems.