Urban road networks in megacities face increasing vulnerability to disruptions that can severely impair mobility and accessibility. Assessing the resilience of such systems requires identifying critical links whose congestion/failures disproportionately degrade network performance. However, conventional link-criticality analysis (LCA) approaches often require exhaustive traffic reassignment, making them computationally impractical for large-scale applications. This study introduces a scalable, data-driven framework for LCA that integrates deep learning (DL) and global sensitivity analysis (GSA) to efficiently quantify link-level vulnerability in metropolitan road networks. The framework formulates LCA as a mapping from network topology, geometric attributes, and traffic-demand features to a composite criticality index that captures both operational degradation and accessibility loss. A DL model is trained on simulation-based disruption scenarios to approximate the impact of network performance, thereby replacing computationally intensive traffic assignment procedures. Subsequently, GSA is applied to interpret the influence and interactions of the underlying factors that drive criticality predictions. The proposed approach is demonstrated on the Greater Cairo road network using a detailed, multi-class model calibrated with observed traffic data. Results show that the DL surrogate accurately reproduces network efficiency and travel-time loss metrics while achieving orders-of-magnitude reductions in computation time compared with traditional LCA. GSA results highlight a limited subset of topologically central and highly loaded corridors as primary drivers of system vulnerability, revealing non-linear interactions among capacity, redundancy, and demand patterns. These findings underscore the potential of combining DL with GSA for interpretable, scalable, and policy-relevant LCA supporting resilient transport planning, investment prioritization, and emergency response in complex urban systems.