Online map construction is essential for autonomous robots to navigate in unknown environments. However, the presence of dynamic objects may introduce artifacts into the map, which can significantly degrade the performance of localization and path planning. To tackle this problem, a novel online dynamic object removal framework for static map construction based on conservative free space estimation (FreeDOM) is proposed, consisting of a scan-removal front-end and a map-refinement back-end. First, we propose a multi-resolution map structure for fast computation and effective map representation. In the scan-removal front-end, we employ raycast enhancement to improve free space estimation and segment the LiDAR scan based on the estimated free space. In the map-refinement back-end, we further eliminate residual dynamic objects in the map by leveraging incremental free space information. As experimentally verified on SemanticKITTI, HeLiMOS, and indoor datasets with various sensors, our proposed framework overcomes the limitations of visibility-based methods and outperforms state-of-the-art methods with an average F1-score improvement of 9.7%.