In bridge widening and reconstruction projects, impact drilling was widely adopted for its high efficiency； however, the strong transient dynamic loads it induces could compromise the stability of adjacent pile foundations. To investigate these effects, this study based on the Liyuan–Dongxiang section of the Hukun Expressway integrated field measurements, finite-element (FE) simulation, and an improved BP neural network and developed an intelligent surrogate for pile dynamic response. Monitoring data were used to calibrate the FE model； multiple working conditions were then generated and time-domain indicators such as measurement-point velocity were extracted. On this basis, Latin hypercube sampling (LHS) was introduced to optimize the training samples and the initialization of the BP network’s weights and biases, yielding an LHS-BP (Latin Hypercube Sampling–Backpropagation Neural Network) model for rapid prediction and correlation analysis of pile responses under varying conditions. Results show that the measured pile velocity exhibited an exponential decay with increasing borehole depth. Compared with a conventional BP model, the LHS-BP model achieved markedly higher predictive accuracy and generalization, with predicted curves closely matching the target values. Pearson correlation analysis further indicated that borehole depth and load intensity are the primary controlling factors, whereas drilling distance and pile diameter had relatively weaker influence. This study elucidated the time-domain response characteristics of the pile–soil system under impact loading and provided theoretical support and engineering guidance for safety control during bridge widening and adjacent pile construction.