Building damage identification shortly after a disaster is crucial for guiding emergency response and recovery efforts. Although optical satellite imagery is commonly used for disaster mapping, its effectiveness is often hampered by cloud cover or the absence of pre-event acquisitions. To overcome these challenges, we introduce a novel multimodal deep learning (DL) framework for detecting building damage using single-date very high resolution (VHR) Synthetic Aperture Radar (SAR) imagery from the Italian Space Agency (ASI) COSMO SkyMed (CSK) constellation, complemented by auxiliary geospatial data. Our method integrates SAR image patches, OpenStreetMap (OSM) building footprints, digital surface model (DSM) data, and structural and exposure attributes from the Global Earthquake Model (GEM) to improve detection accuracy and contextual interpretation. Unlike existing approaches that depend on pre and post event imagery, our model utilizes only post event data, facilitating rapid deployment in critical scenarios. The framework effectiveness is demonstrated using a new dataset from the 2023 earthquake in Turkey, covering multiple cities with diverse urban settings. Results highlight that incorporating geospatial features significantly enhances detection performance and generalizability to previously unseen areas. By combining SAR imagery with detailed vulnerability and exposure information, our approach provides reliable and rapid building damage assessments without the dependency from available pre-event data. Moreover, the automated and scalable data generation process ensures the framework's applicability across diverse disaster-affected regions, underscoring its potential to support effective disaster management and recovery efforts. Code and data will be made available upon acceptance of the paper.