This work presents a deep learning–assisted framework for efficient bandgap calculation and optimization of one-dimensional phononic crystals (1-D PnCs). The considered PnC consists of a periodic unit cell composed of four layers made from three engineering materials—concrete, soil, and rubber—selected for their relevance in vibration isolation and wave attenuation applications. The material properties and layer thicknesses are treated as design variables governing the bandgap characteristics. To address the high computational cost of conventional dispersion solvers, a supervised deep learning surrogate model is developed to replace the transfer matrix method traditionally used for bandgap calculations. The neural network is trained on a large dataset generated using the transfer matrix method and learns the nonlinear relationship between the design variables and the corresponding bandgap boundaries. The trained model demonstrates high predictive accuracy, with more than 95% of the test samples exhibiting errors below 1% when compared with transfer-matrix-based results. To further enable rapid bandgap optimization, the surrogate model is integrated with a genetic algorithm, forming a hybrid optimization framework that efficiently explores the design space without repeated calls to computationally expensive physics-based solvers. The proposed approach achieves a substantial reduction in computational time: optimizing the bandgap using the transfer matrix method requires approximately 7200 seconds, whereas the deep learning–assisted optimization completes the task in only 2.7 seconds. Despite this dramatic acceleration, the discrepancy between the optimized bandgaps predicted by the surrogate model and those recalculated using the transfer matrix method remains below 1%. The results demonstrate that deep learning can serve as an accurate and efficient surrogate for bandgap calculation and optimization in phononic crystal design. The proposed framework significantly accelerates the design process while maintaining high fidelity, and it can be readily extended to more complex periodic structures and higher-dimensional phononic crystals.