  Thermal MeV neutrino emission from core-collapse supernovae offers a unique
opportunity to probe physics beyond the Standard Model in the neutrino sector.
The next generation of neutrino experiments, such as DUNE and Hyper-Kamiokande,
can detect $\mathcal{O}(10^3)$ and $\mathcal{O}(10^4)$ neutrinos in the event
of a Galactic supernova, respectively. As supernova neutrinos propagate to
Earth, they may interact with the local dark matter via hidden mediators and
may be delayed with respect to the initial neutrino signal. We show that for
sub-MeV dark matter, the presence of dark matter-neutrino interactions may lead
to neutrino echoes with significant time delays. The absence or presence of
this feature in the light curve of MeV neutrinos from a supernova allows us to
probe parameter space that has not been explored by dark matter direct
detection experiments.
