Near-real-time estimation of damages (a.k.a, damage nowcasting) to building and infrastructure is crucial during response and recovery efforts. Despite advancements in flood risk predictions, the majority of existing methods primarily focus on inundation estimation with limited damage nowcasting capabilities. Flooding damage nowcasting at fine spatial resolutions remains a very challenging problem with currently no existing model to perform the task. This limitation is mainly due to a number of technical challenges such as limited consideration of non-linear interactions between flood hazards and build-environment features, issues with imbalanced datasets, and the absence of reliable ground truth for model performance evaluation. To address this important gap, this study presents FloodDamageCast, a machine learning (ML) framework tailored for property flood damage nowcasting. The framework leverages heterogeneous data related to the built environment, topographic, and hydrological features to predict residential flood damage in a fine resolution of 500 m by 500 m in the context of Harris County, TX, during the 2017 Hurricane Harvey. To deal with data imbalance, FloodDamageCast includes a tabular data augmentation model based on Conditional Tabular Generative Adversarial Networks (CTGAN). The data augmentation model component addresses highly imbalanced class issues, where the majority class constitutes 96.4% of the dataset, potentially impairing model performance, By combining GAN-based data augmentation with an efficient ML model, Light Gradient-Boosting Machine (LightGBM), our results demonstrate the framework's ability to identify high-damage spatial areas that would be overlooked by baseline models. the satisfactory performance of FloodDamageCast also shows its capability to be used for flood damage nowcasting at a fine spatial resolution to inform response and recovery efforts. The insights from flood damage nowcasting would help emergency management agencies and public officials to more efficiently identify repair needs and allocate resources, and also save time and efforts during on-the-ground inspections.