Aiming to address the issue of low hydraulic performance in low-specific-speed stamping centrifugal pumps, focusing on the CDL1 multi-stage stamping centrifugal pump, using its first-stage impeller as the research object, by combining numerical simulation and experimental testing methods, a comprehensive analysis of the hydraulic performance of the first-stage impeller was conducted. Given that the hydraulic performance of low-specific-speed impellers was influenced by multiple factors, Latin hypercube sampling (LHS) was employed to sample various design variables of the first-stage impeller, forming a sample space and obtaining the corresponding performance parameters. A Kriging surrogate model was then established to analyze the sensitivity of each parameter to the hydraulic performance of the impeller. The critical influence parameters of the impeller were selected as the input for the particle swarm optimization algorithm (PSO), and multi-parameter optimization design was carried out. On this basis, the hydraulic performance and internal flow mechanism of the impeller were investigated in depth. The results showed that the hydraulic performance of the optimized impeller was significantly improved compared with the original design, with the efficiency at the rated point increased by 2.8 percentage points and the single-stage head increased by 0.4m. Additionally, the optimization process revealed that the impeller’s blade angle, inlet and outlet diameters, and blade thickness were the most sensitive parameters affecting hydraulic performance. The improved design not only significantly enhanced the overall efficiency and head but also optimized the flow distribution, reduced turbulence, minimized energy losses, improved fluid dynamics, and increased operational stability, leading to better performance, reliability, and long-term durability in practical applications.