As a key pressure-bearing component of a cubic press, the hinge-beam structure is subjected to a multi-stage ultra-high-pressure synthesis process, including pressure ramp-up and pressure holding. The lug region is prone to fatigue fracture, which makes the requirements for larger-scale cubic presses difficult to satisfy. Real-time monitoring of the hinge-beam structure can be achieved through the rapid acquisition of stress and strain under different operating conditions based on real-time simulation. A method integrating a finite element simulation model of the hinge beam, a lightweight digital twin model, and a global surrogate model was established, and a real-time simulation method for the hinge-beam structure of a cubic press was proposed. Firstly, a finite element simulation of the hinge-beam structure was performed, and a mesh simplification algorithm based on edge collapse and an improved quadric error metric was adopted to generate a lightweight virtual simulation model. Then, a global surrogate model based on the random forest (RF) algorithm was constructed to achieve fast prediction and high-accuracy estimation of the structural state. Finally, a digital twin platform for real-time state assessment of the hinge-beam structure was developed. Experimental results demonstrate that a coefficient of determination of 0.98 is achieved by the surrogate model, and the average evaluation time is approximately 48 ms per prediction, indicating a balance between real-time performance and computational accuracy.