RES-NOVA is a newly proposed experiment for detecting neutrinos from astrophysical sources, mainly Supernovae, using an array of cryogenic detectors made of PbWO crystals produced from archaeological Pb. This unconventional material, characterized by intrinsic high radiopurity, enables low-background levels in the region of interest for the neutrino detection via Coherent Elastic neutrino-Nucleus Scattering (CENS). This signal lies at the detector energy threshold, O(1 keV), and it is expected to be hidden by naturally occurring radioactive contaminants of the crystal absorber. Here, we present the results of a radiopurity assay on a 0.84 kg PbWO crystal produced from archaeological Pb operated as a cryogenic detector. The crystal internal radioactive contaminations are: Th <40 Bq/kg, U <30 Bq/kg, Ra 1.3 mBq/kg and Pb 22.5 mBq/kg. We also present a background projection for the final experiment and possible mitigation strategies for further background suppression. The achieved results demonstrate the feasibility of realizing this new class of detectors.