  Time of flight delay in the supernova neutrino signal offers a unique tool to
set model-independent constraints on the absolute neutrino mass. The presence
of a sharp time structure during a first emission phase, the so-called
neutronization burst in the electron neutrino flavor time distribution, makes
this channel a very powerful one. Large liquid argon underground detectors will
provide precision measurements of the time dependence of the electron neutrino
fluxes. We derive here a new $\nu$ mass sensitivity attainable at the future
DUNE far detector from a future supernova collapse in our galactic
neighborhood, finding a sub-eV reach under favorable scenarios. These values
are competitive with those expected for laboratory direct neutrino mass
searches.
