In structural engineering, the iterative optimisation of complex timber wall components is fundamentally limited by the prohibitive computational costs of non-linear Finite Element Analysis (FEA). To overcome this bottleneck, this study introduces a highly efficient machine learning-based surrogate model utilising a convolutional encoder–decoder architecture to predict the global buckling load factor (BLF) directly from structural topology. We evaluate three distinct modeling strategies: a Direct prediction model, a Sequential model, and a multitask Dual-Loss model designed to simultaneously predict the BLF and reconstruct spatial tensile stress fields. Experimental results demonstrate that both the Direct and Dual-Loss approaches achieve near-perfect predictive accuracy on in-distribution data, yielding a coefficient of determination (R²) of approximately 0.996. Crucially, these surrogates accelerate inference times by a factor of roughly 12,800 compared to traditional iterative solvers, reducing evaluation times from hours to mere seconds. Furthermore, the models exhibit exceptional robustness and extrapolative capability under rigorous out-of-distribution testing. The models maintain high predictive fidelity when subjected to cross-dataset distributional shifts (R² $\approx 0.94$) and when evaluating intentionally low-performing, highly vulnerable configurations (R²$\approx 0.967$). Extensive validation on structurally disjoint, hold-out wall geometries confirms the models’ ability to generalise to entirely unseen topologies without introducing systematic bias (R²$>0.95$). By successfully internalising the underlying physical principles of load redistribution, this surrogate framework provides a reliable, computationally inexpensive foundation for enabling real-time, autonomous generative design and structural optimisation.