Link criticality analysis (LCA) in transportation networks plays a pivotal role in assessing the systemic impact of link failures on overall traffic performance. Traditional LCA approaches often rely on exhaustive link-removal simulations or graph-theoretic metrics, which become computationally prohibitive and behaviorally simplistic when addressing multiple link failures. This study proposes a novel, scalable framework that integrates stochastic user equilibrium traffic assignment, deep-learning-based flow estimation using stacked autoencoders (SAEs), and multi-method global sensitivity analysis (GSA) to evaluate network-wide link importance. The framework generates synthetic demand scenarios using Monte Carlo simulations, applies a stochastic assignment model to estimate flow distributions, and trains an SAE model to predict average user delay. The trained model then enables efficient GSA to quantify the influence of each link. The methodology is applied to a real-world case study in Egypt’s New Capital. The proposed framework demonstrates high predictive accuracy (mean standard error = 0.66, R² = 0.98) and computational efficiency, making it suitable for large-scale, data-sparse, or developing urban contexts. GSA results reveal critical links with both direct and nonlinear effects on delay, guiding planners toward strategic investments and resiliency planning. This integrated approach advances LCA by offering interpretable, scalable, and data-driven insights into transportation network vulnerabilities.