Rare-earth metal oxides (REMOs) exhibit distinctive properties, among which cerium oxide (CeO2) displays numerous industrial, technological, and medical applications. However, the inclusion of hafnium (Hf) at the cerium (Ce) site to form the (Ce1-ₓHfₓO2) lattice system at a concentration of x = 0.25 would have an impact on enhancing the physical properties of the simulated configuration. Density functional theory (DFT) was used to perform the calculations, supported by the Hubbard correction factor (U). The generalized gradient approximation (GGA-PBE) was employed to analyze the electronic, structural, optical, and mechanical properties at hydrostatic pressures (P = 0, 25, 50, 75, and 100 GPa). The ground state geometry of the pristine fluorite CeO2 corresponds to 5.438 Å, signifying an excellent agreement with the available published literature. The calculated lattice parameter of Ce0.75Hf0.25O2 is diminished to 5.327 Å as compared with CeO2. Furthermore, CeO2 exhibits a semiconductor character with a direct band gap of 3.134 eV, while the band gap of the Ce0.75Hf0.25O2 system was reported to be 3.073 eV, demonstrating slight degradation. However, under pressure, the results demonstrate a gradual increment in the band gap energy of Ce0.75Hf0.25O2 until reaching 3.861 eV at 100 GPa. Furthermore, the thermodynamic feasibility was investigated via the chemical potential approach. The pressure-dependent optical properties were extensively discussed of Ce0.75Hf0.25O2, demonstrating enhanced optical properties in the ultraviolet (UV) region, motivating its suitable utility for optoelectronic memristors and other photonic applications.