Hybrid improper ferroelectricity with quasi-two-dimensional (quasi-2D) structure has attracted much attention recently due to its great potential in realizing strong magnetoelectric coupling and room-temperature multiferroicity in a single phase. However, recent studies show that there appears high coercive field and low remnant polarization in ceramics, which severely hinders the applications of this material. In this work, high-quality Sr₃Sn₂O₇ and Sr₃Sn_1.99Ge_0.01O₇ ceramics with a Ruddlesden-Popper (R-P) structure are successfully prepared, and their crystal structures and electrical properties are investigated in detail. It is found that the Sr₃Sn₂O₇ ceramic exhibits a lower coercive field that is close to that of Sr₃Sn₂O₇ single crystal. Moreover, via a small amount of Ge doping, the polarization reaches 0.34 μC/cm² for Sr₃Sn₂O₇ and 0.61 μC/cm² for Sr₃Sn_1.99Ge_0.01O₇. Combining crystal lattice dynamic studies, we analyze the Raman and infrared responses of the samples, showing the information about the tilting and rotation of the oxygen octahedra in the samples. The improved ferroelectricity after doping may be attributed to the increased amplitude of the tilt mode and the reduced amplitude of rotation mode. Besides, the enhanced ferroelectric properties through Ge doping and its mechanism are further investigated by the Berry phase approach and the Born effective charge method. Furthermore, via the UV-visible spectra, the optical bandgap is determined to be 3.91 eV for Sr₃Sn₂O₇ ceramic and 3.95 eV for Sr₃Sn_1.99Ge_0.01O₇ ceramic. Using the Becke-Johnson potential combined with the local density approximation correlation, the bandgap is calculated and is found to be in close agreement with the experimental result. And the electronic excitations can be assigned to the charge transfer excitation from O 2p to Sn 5s (Ge 4s). The effects of Ge doping on the ability of Sr₃Sn₂O₇ to gain and lose electrons and the bonding strength of Sn-O bond are analyzed via two-dimensional charge density difference. In conclusion, this study provides insights into the synthesis method and modulation of ferroelectric properties of hybrid improper ferroelectrics Sr₃Sn₂O₇, potentially facilitating their widespread applications in various capacitors and non-volatile memory devices.