  We consider a scenario in which dark matter particles are accelerated to
semi-relativistic velocities through their scattering with the Diffuse
Supernova Neutrino Background. Such a subdominant, but more energetic dark
matter component can be then detected via its scattering on the electrons and
nucleons inside direct detection experiments. This opens up the possibility to
probe the sub-GeV mass range, a region of parameter space that is usually not
accessible at such facilities. We analyze current data from the XENONnT and
LUX-ZEPLIN experiments and we obtain novel constraints on the scattering cross
sections of sub-GeV boosted dark matter with both nucleons and electrons. We
also highlight the importance of carefully taking into account Earth's
attenuation effects as well as the finite nuclear size into the analysis. By
comparing our results to other existing constraints, we show that these effects
lead to improved and more robust constraints.
