This paper investigates the application of a wheel-spoke cable-supported grid structure in stadium construction, with a particular focus on the technical challenges associated with the “cables-first, steel-second” construction method. This method requires the installation of the upper steel structure while being supported by a flexible cable net. Due to the inherent flexibility of the cable net, special technical measures must be implemented during the installation process. In particular, during the hoisting of the first radial steel beam, in addition to considering conventional hoisting parameters, the lateral stability of the structure must be carefully addressed. Based on the structural characteristics of the project and on-site construction conditions, a finite element analysis (FEA) is conducted to simulate the installation process of the first radial steel beam supported by the flexible cable net. Furthermore, a full-scale hoisting test is carried out to validate the numerical analysis results. The study reveals that by appropriately adjusting the tension of the downward pull assembly cables, optimizing the hoisting sequence, and implementing the lateral stability measures proposed in this paper, the construction method can ensure the safe installation of radial steel beams on the cable net. The experimental results closely align with the theoretical analysis, verifying the accuracy of the computational method. The findings of this study provide theoretical support and practical guidance for the successful implementation of the Guangzhou Football Park Stadium project and offer valuable insights into construction techniques for large-span cable-supported grid structures.