To enhance the efficiency of stochastic vibration analysis for the Train-Track-Bridge (TTB) coupled system, this paper proposes a prediction method based on a Genetic Algorithm-optimized Backpropagation (GA-BP) neural network. First, initial track irregularity samples and random parameter sets of the Vehicle–Bridge System (VBS) are generated using the stochastic harmonic function method. Then, the stochastic dynamic responses corresponding to the sample sets are calculated using a developed stochastic vibration analysis model of the TTB system. The track irregularity data and vehicle–bridge random parameters are used as input variables, while the corresponding stochastic responses serve as output variables for training the BP neural network to construct the prediction model. Subsequently, the Genetic Algorithm (GA) is applied to optimize the BP neural network by considering the randomness in excitation and parameters of the TTB system, improving model accuracy. After optimization, the trained GA-BP model enables rapid and accurate prediction of vehicle–bridge responses. To validate the proposed method, predictions of vehicle–bridge responses under varying train speeds are compared with numerical simulation results. The findings demonstrate that the proposed method offers notable advantages in predicting the stochastic vibration response of high-speed railway TTB coupled systems.