The C4F7N/CO2 gas mixture is currently regarded as the most promising alternative to SF6 and is intended for use in high-voltage gas-insulated equipment. Surface flashover phenomena occurring in such equipment pose significant risks to both the operational lifespan of the devices and the safety and stability of the power system. To clarify the underlying mechanisms and guide experimental investigations aimed at enhancing the surface insulation strength, this study employs the finite element method to construct a DC voltage surface flashover model of a 3.5% C4F7N/96.5% CO2 gas mixture. The model comprehensively accounts for gas-phase processes including molecular desorption and collision ionization, the accumulation of surface charges at the gas-solid interface, and the influence of carrier detrapping in the solid dielectric. The surface flashover process under highly non-uniform electric fields is systematically investigated. Based on the simulation results, it is concluded that under an applied voltage, the formation mechanisms of streamers on the anode and cathode sides differ due to the electrode polarity and the dominant charged particles at the streamer head, with electron emission from the cathode triple junction via a jet-like mechanism identified as the primary cause.