  We propose a novel strategy to search for new physics in timing spectra,
envisioning the situation in which a new particle comes from the decay of its
heavier partner with a finite particle width. The timing distribution of events
induced by the dark matter particle scattering at the detector may populate in
a relatively narrow range, forming a "resonance-like" shape. Due to this
structural feature, the signal may be isolated from the backgrounds, in
particular when the backgrounds are uniformly distributed in energy and time.
For proof of the principle, we investigate the discovery potential for dark
matter from the decay of a dark photon in the COHERENT experiment, and show the
exciting prospects for exploring the associated parameter space with this
experiment. We analyze the existing CsI detector data with a timing cut and an
energy cut, and find, for the first time, an excess in the timing distribution
which can be explained by such dark matter. We compare the sensitivity to the
kinetic mixing parameter ($\epsilon$) for current and future COHERENT
experiments with the projected limits from LDMX and DUNE.
