The speed of 400 km/h represents a milestone that humanity has been striving for in wheel-rail high-speed railway systems, and the research is extremely challenging. In this study, a sophisticated rigid-flexible coupled dynamic model of a vehicle–track spatial nonlinear coupling system is developed. The model incorporates the elastic deformation and three-dimensional vibrations of the rail, track slab, and concrete base, while the vehicle is simplified as a rigid body with 31 degrees of freedom. The “Trace Method” and the “Minimum Distance Method” are employed to identify the spatial contact points between the wheel and rail, followed by a quasi-elastic contact correction. Based on this, the geometric relationship of the wheel-rail spatial contact is established. Given the complexity of the dynamic behavior in the vehicle–track coupling system and the computational cost associated with locating the spatial contact points, an improved cross-iteration algorithm is developed and a numerical approach is proposed. By integrating the Trace Method into the cross-iteration process, this strategy significantly improves both computational efficiency and model accuracy. As an application case, the adaptability of existing Chinese high-speed railways to operate at 400 km/h under track random irregularity excitation is investigated, and the dynamic performance of the coupled high-speed train–track system is evaluated.