The initial water-oxidation reaction mechanism of the hydrated cobalt phosphate (CoPi) co-catalyst, which is consistent with conventional experimental findings, is investigated for O-O bond and OOH formation in this study. Theoretical calculations of hydrated CoPi cluster models, which are validated by vibrational spectrum calculations, elucidate the roles of phosphate as a source of oxygen and deliverer of protons, both of which result in the spontaneous formation of an O-O bond after the release of two electrons and two protons. The calculations also show that OOH formation proceeds subsequently depending on the spin electronic states of the hydrated CoPi surface, and O2 formation then spontaneously progresses after the release of two electrons and two protons. By theoretically tracing these processes, the initial water-oxidation reaction mechanism of the hydrated CoPi co-catalyst is proposed.