We theoretically investigate the structural stability, electronic property, and superconductivity of the hydrogen-rich compound Li\(_{2}\)CuH\(_{6}\) in its face-centered cubic phase. First-principles calculations show that Li\(_{2}\)CuH\(_{6}\) is thermodynamically metastable at ambient pressure but dynamically stable. Moreover, ab initio molecular dynamics (AIMD) simulation at 300 K further confirms that Li\(_{2}\)CuH\(_{6}\) remains structurally intact without decomposition. These results suggest that the material may be synthesized under high pressure and retained after decompression. Although thermodynamically metastable at ambient conditions, its dynamic stability supports its persistence after pressure release. Moreover, Li\(_{2}\)CuH\(_{6}\) exhibits metallic behavior with a flat band and van Hove singularity (vHS) near the Fermi level and Fermi-surface states dominated by Cu–d and H–s orbitals. Phonon calculations further indicate that hydrogen vibrations dominate the phonon contribution, while the electronic states near the Fermi level govern the coupling strength, resulting in a large electron–phonon coupling constant. Insights into the superconducting temperature (\(T_\textrm{c}\)) are obtained using various theoretical approaches, which estimate \(T_\textrm{c}\) to be in the range of 93–152 K. Bonding analysis further indicates mixed covalent–ionic character within Cu–H octahedra. These results highlight Li\(_{2}\)CuH\(_{6}\) as a promising hydrogen-based metastable superconductor for future experimental exploration.