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Hybrid interfaces formed by inorganic semiconductors and organic molecules are intriguing materials for opto-electronics. Interfacial charge transfer is primarily responsible for their peculiar electronic structure and optical response. Hence, it is essential to gain insight into this fundamental process also beyond the static picture. Ab initio methods based on real-time time-dependent density-functional theory coupled to the Ehrenfest molecular dynamics scheme are ideally suited for this problem. We investigate a laser-excited hybrid inorganic/organic interface formed by the electron acceptor molecule 2,3,5,6-tetrafluoro-7,7,8,8-tetracyano-quinodimethane (F4TCNQ) physisorbed on a hydrogenated silicon cluster, and we discuss the fundamental mechanisms of charge transfer in the ultrashort time window following the impulsive excitation. The considered interface is $p$-doped and exhibits charge transfer in the ground state. When it is excited by a resonant laser pulse, the charge transfer across the interface is additionally increased, but contrary to previous observations in all-organic donor/acceptor complexes, it is not further promoted by vibronic coupling. In the considered time window of 100~fs, the molecular vibrations are coupled to the electron dynamics and enhance intramolecular charge transfer. Our results highlight the complexity of the physics involved and demonstrate the ability of the adopted formalism to achieve a comprehensive understanding of ultrafast charge transfer in hybrid materials.