In this letter, we report the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin-orbit coupling. We achieve this in high-mobility hBN-encapsulated SLG/WSe2 heterostructures through measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along with a substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, we uncover evidence of a bandgap opening and band inversion in the SLG. Further, we establish that the deviation of the low-energy band structure from pristine SLG is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane-Mele SOC being inconsequential. Despite robust theoretical predictions and observations of band-splitting, a quantitative measure of the spin-splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in SLG was missing -- our combined experimental and theoretical study fills this lacuna.