We investigate a scenario in which sub-GeV dark matter (DM) particles acquire semi-relativistic velocities through scattering with the Diffuse Supernova Neutrino Background (DSNB). This mechanism introduces high-energy DM particles capable of producing detectable recoil signals in underground detectors. Analyzing the data from XENONnT and LUX-ZEPLIN (LZ) experiments, we place new constraints on the scattering cross-sections of sub-GeV DM with electrons and nucleons. We also highlight the necessity of considering Earth’s attenuation effects and finite nuclear size for nuclear scattering, and we also compare our results with existing limits, underscoring the significance of these data in probing the sub-GeV DM parameter space.