Pressure sensors are prone to failure in complex environments, making it difficult to reliably obtain the internal air pressure of inflated beams and hindering accurate assessment of their load-bearing capacity. To address this issue, an indirect prediction method for the ultimate load-bearing capacity of inflated beams is proposed by integrating experimental data with a surrogate model. A finite element model was established in ABAQUS, and the post-buckling behavior of the inflated beam was characterized in different stages using the ratio of tangent stiffness. Based on this characterization, the concept of the initial buckling stage was proposed and defined as a response interval that simultaneously exhibits high pressure sensitivity and sufficient residual load-carrying capacity. A multi-objective optimization framework was employed to balance the total Fisher information of the internal pressure against the mean residual load-carrying capacity, thereby determining the range of this interval. A neural-network-based surrogate model was developed to enable rapid prediction of load responses. The load–deflection data within the initial buckling stage were then incorporated into a Bayesian inference framework to estimate the internal pressure and subsequently predict the load-carrying limit. The results show that the posterior distribution of the internal pressure exhibits a unimodal characteristic with substantially reduced uncertainty, and the prediction error of the load-carrying limit based on the posterior mean is 4.86%. The proposed method provides a feasible approach for evaluating the load-carrying capacity of inflated structures under conditions where pressure sensors are unavailable or have failed.