<p>This study presents a detailed first-principles investigation of the structural, elastic, electronic, optical, and thermoelectric properties of the double perovskite Pb₂CoMoO₆ compound. The calculations were carried out the full-potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). We evaluated the energetic stability, the Goldschmidt tolerance factor (<i>t</i>_<i>G</i>​), octahedral factor (<i>µ</i>), and modified tolerance factor (<i>τ</i>), formation energy (<i>ΔH</i>_<i>f</i>), cohesive energy (<i>E</i>_<i>coh</i>), phonon dispersion and mechanical characteristics. The findings confirm that Pb₂CoMoO₆ crystallizes in a perfectly cubic structure belonging to the Fm-3&#xa0;m space group. Mechanical analysis indicates high elasticity and strength as evidenced by high mass and Young’s moduli, which indicative the stability of the material. The electronic structure calculations reveal half-metallic ferromagnetic (HMF) behavior, with a spin-up band gap of 1.558&#xa0;eV along the L-Γ direction under the GGA + U approach. Additionally, the compound exhibits an integer magnetic moment of 3.0 <i>µ</i>_<i>B</i> per formula unit. Moreover, Pb₂CoMoO₆ exhibits strong optical absorption in the ultraviolet (UV) spectrum and displays promising thermoelectric behavior, with favorable Seebeck coefficients and a high figure of merit (<i>ZT</i>_<i>max</i>≈1) at room temperature, suggesting potential for applications in spintronic and thermoelectric devices.</p>