With the continuous improvement of the requirements for water ecological and water environment friendliness, intelligence, and landscaping in water conservancy project construction, the application of steel structures in hydraulic structures has become increasingly widespread. As a high-load-bearing connection node of steel-concrete structures, the prestressed steel-concrete joint has broad application scenarios in the fields of water conservancy engineering and even structural engineering. This study relies on the prestressed steel-concrete joint at the connection between the main girder of a special-shaped cable-stayed bridge and the pedestrian bridge of a cross-sea bridge-lock project in Hainan Province. Through parametric nonlinear simulation analysis, taking the thickness of the steel box plate, the height of the steel box, the insertion depth of the steel box into the concrete, and the vertical load as independent variables, and the vertical displacement of the joint as the dependent variable, 20,774 pieces of effective data were collected. On this basis, the Support Vector Machine (SVM) method, Random Forest method, and Deep Neural Network (DNN) method in machine learning were respectively used. With 4-dimensional input features and 1-dimensional output labels set, the aforementioned samples were used for training and testing to form an engineering structure surrogate model. The results show that the performance evaluation index R2 of the three regression methods is 0.953, 0.997, and 0.999 respectively. Among the performances of the nonlinear load-displacement curves of the test set, the DNN method has the best prediction effect, reflecting the strong adaptability of the DNN method in the data-driven engineering structure surrogate model. The surrogate model empowers the refined and rapid design of multiple prestressed steel-concrete joint structures in this project, saving a large amount of computing power and time costs compared with the traditional finite element method.