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AT 2018cow was the nearest and best studied example of a new breed of extra-galactic, luminous and rapidly-evolving transient. Both the progenitor systems and explosion mechanisms of these rapid transients remain a mystery - the energetics, spectral signatures, and timescales make them challenging to interpret in established classes of supernovae and tidal disruption events. The rich, multi-wavelength data-set of AT 2018cow has still left several interpretations viable to explain the nature of this event. In this paper we analyse integral-field spectroscopic data of the host galaxy, CGCG 137-068, to compare environmental constraints with leading progenitor models. We find the explosion site of AT 2018cow to be very typical of core-collapse supernovae (known to form from stars with MZAMS ~8-25M), and infer a young stellar population age at the explosion site of few times 10Myr, at slightly sub-solar metallicity. When comparing to expectations for exotic intermediate-mass black hole (IMBH) tidal disruption events,we find no evidence for a potential host system of the IMBH. In particular, there are no abrupt changes in metallicity or kinematics in the vicinity of the explosion site, arguing against the presence of a distinct host system. The proximity of AT 2018cow to strong star-formation in the host galaxy makes us favour a massive stellar progenitor for this event.