With the enhancement of safety performance requirements in the car manufacturing field, the quality standards for the sheet molding process have imposed higher demands. However, during the pressure-building phase of pump-controlled hydraulic die cushion systems, the combined effects of high-order dynamics, system uncertainties, and strong nonlinearities pose significant challenges to maintaining precise control and dynamic response performance of the blank holder force (BHF). To address these challenges, we propose an intelligent model predictive control (MPC) strategy that synergistically integrates an extended state observer (ESO) for disturbance compensation with parameters optimized by a genetic algorithm (GA). The mathematical model and state-space model of the system are established. Subsequently, the ESO is integrated with MPC to enable active compensation for internal and external disturbances. The GA is employed to optimize the controller parameters within the MPC framework. Finally, a simulation testbed for the pump-controlled hydraulic die cushion experimentally validates the process. Experimental results demonstrate that compared to MPC and conventional PID control, the proposed strategy achieves significant reductions in pressure overshoot (0.87% and 1.8% at 100 bar; 3.3% and 5.9% at 200 bar), pressure-building time (13.9% and 31.4% at 100 bar; 6.7% and 11.5% at 200 bar), and stroke length (10.5% and 32% at 100 bar; 11.5% and 28.1% at 200 bar). This validates its effectiveness in enhancing both control precision and dynamic response performance, providing a reliable solution for large-scale applications of pump-controlled hydraulic die cushions in high-dynamic stamping scenarios.