Climate change results in an increased probability of extreme weather events that put societies and businesses at risk on a global scale. Therefore, near real-time mapping of natural hazards is an emerging priority for the support of natural disaster relief, risk management, and informing governmental policy decisions. Recent methods to achieve near real-time mapping increasingly leverage deep learning (DL). However, DL-based approaches are designed for one specific task in a single geographic region based on specific frequency bands of satellite data. Therefore, DL models used to map specific natural hazards struggle with their generalization to other types of natural hazards in unseen regions. In this work, we propose a methodology to significantly improve the generalizability of DL natural hazards mappers based on pre-training on a suitable pre-task. Without access to any data from the target domain, we demonstrate this improved generalizability across four U-Net architectures for the segmentation of unseen natural hazards. Importantly, our method is invariant to geographic differences and differences in the type of frequency bands of satellite data. By leveraging characteristics of unlabeled images from the target domain that are publicly available, our approach is able to further improve the generalization behavior without fine-tuning. Thereby, our approach supports the development of foundation models for earth monitoring with the objective of directly segmenting unseen natural hazards across novel geographic regions given different sources of satellite imagery.