Timing-driven layer assignment during global routing significantly impacts delay and congestion. Traditional methods rely on iterative heuristics with repeated timing and congestion analysis under the hood, leading to high runtime and limited scalability for modern designs. We present a hybrid machine learning (ML) framework that combines graph convolutional networks (GCNs) and convolutional neural networks (CNNs) for fast, timing- and congestion-driven layer assignment. GCNs model netlist connectivity and timing-critical paths, while CNNs extract spatial features such as capacity and utilization maps across the metal layer stack from a placed layout. Formulated as a multi-class classification problem, our model predicts the layer for every Steiner tree edge of a net. The ML model is trained on timing and congestion-driven global-routed layout data to predict optimized layer assignments rapidly in a single pass. Experiments on benchmark designs demonstrate that our approach improves worst-case and total negative slack post detailed route while achieving a speedup compared to traditional congestion and timing-driven methods.