To realize the new vision of space exploration, the capacity of the new generation of manned spacecraft is significantly increased, which results in greater impact load during landing. The airbag cushioning system can substantially attenuate the impact acceleration but increases the difficulty of system design and analysis. This paper utilizes the long short-term memory network and the dataset generated by finite element analysis to train a surrogate model for quickly predicting the impact acceleration of the spacecraft when soft landing on the complex airbag cushioning system. Comparison of the prediction results between the finite element analysis and the surrogate model shows that the LSTM-based surrogate model can quickly predict the impact acceleration under the body fixed coordinate system of the spacecraft, especially in the prediction of the longitudinal acceleration along the spacecraft's rotation axis and the transverse acceleration perpendicular to the rotation axis. The relative error between the surrogate model and the finite element analysis is about 10%, but the prediction speed is 100,000 times faster. It is fully proved that the proposed surrogate model can effectively accelerate the design cycle of such rigid-flexible coupled complex systems and improve the efficiency of engineering calculations.