The accuracy of quasiparticle corrections in a single-shot G0W0 calculation relies heavily on the preceding eigensystem of density functional theory (DFT). An incorrect energy spectrum obtained from the DFT calculation can result in an inaccurate quasiparticle G0W0 bandgap. This study explicitly investigates the bandgaps of chalcopyrite semiconductors within G0W0, considering various DFT approximations, including semilocal, hybrid, and nonempirical screened dielectric-dependent hybrid (DDH) as the starting point for G0W0 calculation. The superiority of G0W0 on top of screened DDH is evident in achieving highly accurate bandgaps for chalcopyrite semiconductors. In addition, when the Bethe-Salpeter equation is solved, the optical absorption spectra derived from these calculations are remarkably precise. This study demonstrates that nonempirical G0W0@DDH serves as a cost-effective and precise tool for various applications related to chalcopyrite semiconductors, particularly in cases where a self-consistent GW (scGW) calculation is challenging.