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The discovery of high-temperature superconductivity in hydrogen-rich compounds under extreme pressures has prompted great excitement, intense research, but also debate over the past decade. In this study, we acquired unprecedented high-quality Raman spectra of hexagonal LaH10 at approximately 145 GPa and low temperatures, in conjunction with electrical transport measurements. Upon cooling, we observe a drop of resistivity and simultaneous remarkable variations of phonon frequencies and linewidths. These effects are interpreted and perfectly reproduced by the Migdal–Eliashberg theory, providing a definitive proof of phonon-mediated superconductivity and enabling a quantitative determination of the superconducting energy gap. Our results establish Raman spectroscopy as a robust, contact-free probe with micrometric resolution for studying high temperature superconductivity, opening a powerful route to its discovery and characterization. We acknowledge financial support from the European Union ERC-SYN MORE-TEM no. 951215 (F.M., L.B., P.B. and G.M.).