Rapid and accurate assessment of building damage in sudden-onset disasters is crucial for effective humanitarian assistance and disaster response. However, the occurrence of disasters is highly uncertain, e.g., unexpected geographic location and hazards, which challenge the conventional building damage assessment model on generalization and transferability. Unfortunately, there is little public literature on transferable building damage assessment. This is because assessing building damage using pre- and post-disaster satellite images is a complex, multi-temporal, and multi-task problem. It involves two main subtasks: building localization and damage classification, which are non-trivial to handle with generic transfer learning approaches designed for single-image and single-task problems. On the other hand, post-disaster training image availability in the target domain remains an obstacle since these generic transfer learning methods require pre-/post-disaster image pairs as target training images, resulting in a costly time window (period from obtaining post-event training image to obtaining assessment results) in disaster response. In this paper, we present a single-temporal domain adaptive semantic change detection framework, which frames domain adaptive building damage assessment and only additionally requires target pre-disaster images for adaptation training. Our framework first presents a decoupled task modeling via the equivalent form of prediction error expectations. This enables generic transfer learning methods to be used for domain adaptive building damage assessment. To fundamentally overcome the problem of post-disaster training image availability within our framework, we propose an unsupervised single-temporal change adaptation (STCA) algorithm. The main idea is “damage is everywhere”, which is motivated by the fact that building damage is a change process driven by the disaster event. We leverage target pre-disaster images and source post-disaster images to simulate such semantic change processes to provide training data, fundamentally addressing the post-disaster training image availability issue and avoiding that costly time window. The extensive experiments on global-scale and local-scale study areas suggest that our framework allows most transfer learning approaches to work well on domain adaptive building damage assessment. Our STCA achieves superior performance compared to other transfer learning approaches. More importantly, unlike other approaches that rely on target pre/post-disaster images for adaptation, it requires no target post-disaster training images. This nature significantly improves the availability of STCA in real-world disaster response for the building damage assessment model.