Living in a changing climate, human society now faces more frequent and severe natural disasters than ever before. As a consequence, rapid disaster response during the "Golden 72 Hours" of search and rescue becomes a vital humanitarian necessity and community concern. However, traditional disaster damage surveys routinely fail to generalize across distinct urban morphologies and new disaster events. Effective damage mapping typically requires exhaustive and time-consuming manual data annotation. To address this issue, we introduce Smart Transfer, a novel Geospatial Artificial Intelligence (GeoAI) framework, leveraging state-of-the-art vision Foundation Models (FMs) for rapid building damage mapping with post-earthquake Very High Resolution (VHR) imagery. Specifically, we design two novel model transfer strategies: first, Pixel-wise Clustering (PC), ensuring robust prototype-level global feature alignment; second, a Distance-Penalized Triplet (DPT), integrating patch-level spatial autocorrelation patterns by assigning stronger penalties to semantically inconsistent yet spatially adjacent patches. Extensive experiments and ablations from the recent 2023 Turkiye-Syria earthquake show promising performance in multiple cross-region transfer settings, namely Leave One Domain Out (LODO) and Specific Source Domain Combination (SSDC). Moreover, Smart Transfer provides a scalable, automated GeoAI solution to accelerate building damage mapping and support rapid disaster response, offering new opportunities to enhance disaster resilience in climate-vulnerable regions and communities. The data and code are publicly available at https://github.com/ai4city-hkust/SmartTransfer.