The Bay of Bengal is well known for some of the deadliest cyclones in history. At the same time, storm surge forecasting in this region is physically involved and computationally costly. Here we show a proof of concept of a real-time, computationally efficient, and physically consistent forecasting system with an application to the recent Supercyclone Amphan. While challenges remain, our study paves the path forward to the improvement of the quality of localized forecast and disaster management.