Earthquakes remain among the most destructive and unpredictable natural hazards, posing a major challenge for geohazard mitigation. Recent advances in high-performance computing now enable increasingly realistic simulations of earthquake dynamic rupture and ground shaking. However, the high computational cost of dynamic rupture simulations limits their direct use in near-real-time earthquake response. Here, we present a fully physics-based dynamic rupture forecasting framework designed to overcome these limitations. The proposed workflow relies on a precomputed catalog of high-resolution dynamic earthquake rupture scenarios for a given fault system, enabling rapid event characterization once an earthquake occurs. The workflow consists of two main components. First, a large ensemble of three-dimensional dynamic rupture simulations, together with synthetic seismograms and shake maps, is computed in advance and constrained by seismic, geodetic, and experimental data. Second, when a moderate to large earthquake (magnitude > 6) is detected, an automated rapid-response procedure searches the catalog to identify the scenario(s) that best match early observations, such as recorded seismic waveforms. We demonstrate this approach for the Alto Tiberina fault system, constructing a catalog of 100 data-driven dynamic rupture scenarios by varying a range of key physical parameters. Individual 90-s-long simulations require about 4600 core hours, highlighting the necessity of pre-computing the catalog. By decoupling the computationally intensive simulations from real-time response, this workflow enables source characterization and associated shaking estimates within minutes to hours after a large earthquake. This workflow has been developed as an earthquake Digital Twin component within DT-Geo. Beyond rapid response, the scenario catalog, openly shared via the Geo-INQUIRE Simulation Data Lake, provides a foundation for physics-based seismic hazard assessment and for training reduced-order or scientific machine-learning models capable of near-instantaneous rupture prediction.