We examine a macroscopic system in a quantum superposition of two spatially separated localized states as a detector for a stream of weakly interacting relativistic particles. We do this using the explicit example of neutrinos with $\mathrm{MeV}$-scale energy scattering from a solid object via neutral-current neutrino-nucleus scattering. Presuming the (anti)neutrino source to be a nuclear fission reactor, we utilize the estimated flux and coherent elastic neutrino-nucleus cross section to constrain the spatial separation $\mathrm{\ensuremath{\Delta}}x$ and describe the temporal evolution of the sensing system. Particularly, we find that a potentially measurable relative phase between quantum superposed components is obtained for a single gram scale mass placed in a superposition of spatial components separated by ${10}^{\ensuremath{-}14} \mathrm{m}$ under sufficient cooling and background suppression.