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The observation of substantially enhanced superconducting transition temperatures of single layer FeSe films on SrTiO₃ (STO) substrates has stimulated intensive research to identify the underlying microscopic mechanism. At present, the significant role of interfacial coupling has been widely recognized, but the precise nature of the superconductivity enhancement remains open. By employing high resolution electron energy loss spectroscopy, collective excitations in FeSe/STO system, including the Fuchs-Kliewer (F-K) phonons of STO and the polaronic plasmon originating from collective oscillation of polarons, were measured and studied. With FeSe growth, two dramatic contrasts were observed comparing with bare STO. First, the F-K phonons show indispensable correlation with the polaronic plasmon, indicating F-K phonons participate into the collective oscillation of polarons. Second, the linewidth broadening of the F-K phonons after FeSe growth indicates significant coupling between F-K phonons of STO and electrons in FeSe. It is evidenced that the electrons in FeSe/STO systems are dressed by the strongly polarized local lattice distortions associated with the F-K phonons across the interface. Furthermore, such an interfacial electron-phonon interaction is non-adiabatic in nature, leading to the formation of dynamic interfacial polarons that form the observed polaronic plasmon. The corresponding theoretical model shows that the interfacial polaron-polaron interaction can induce additional attraction between electrons in the systems, resulting in enhanced electron pairing strength and, accordingly, superconductivity.