The precise control of three-dimensional feature profiles during plasma etching is a fundamental challenge in nanoscale device fabrication, directly impacting performance and yield. While conventional physics-based simulations can capture the underlying plasma-surface interactions, their prohibitive computational cost limits their use for large-area analysis or rapid process development. To bridge this gap, we introduce EtchFormer, a Transformer-based deep learning framework engineered as a high-speed virtual metrology engine for 3D etch profile prediction. Crucially, the model is trained on a comprehensive dataset generated by the physically-calibrated, multi-scale TCAD simulations described in our methodology. This dataset, comprising over 50,000 time-resolved frames from thousands of etching sequences, embeds the fundamental physics of ion-enhanced etching, surface passivation, and byproduct transport across a wide spectrum of industrial process conditions and complex nanoscale patterns. The EtchFormer framework demonstrates high-fidelity reconstruction of entire etch sequences (Structural Similarity Index > 0.945) and, critically, exhibits robust long-range forecasting capabilities by accurately extrapolating profile evolution beyond the temporal range of the training data. Validated on complex layouts, EtchFormer reduces the prediction time for a complete sequence from hours to subseconds (~0.3 s). This capability provides a foundation for the virtual metrology, enabling the exploration of complex process-pattern dependencies, the prediction of structural anomalies, and the accelerated design and optimization of etching processes.