For Advanced Air Mobility (AAM) systems operating in diverse environments, redundant localization techniques are essential to ensure continuous and safe mission execution. In this study, we propose a 3D place recognition and pose estimation method for AAM using a hemispherical light detection and ranging (LiDAR) sensor. The proposed approach includes a feature extraction method that leverages height differences in surrounding objects, a method for generating local and global descriptors from feature distances, and an efficient geometric verification and localization process through correspondence calculation. Additionally, the method incorporates a process to create a virtual descriptor database using a point cloud map, enabling robust localization in unvisited areas. All procedures are handcrafted, and the performance of the proposed method is validated through comparison with state-of-the-art methods using datasets generated in a simulator. The proposed method achieved over 99.16% average precision (AP) and a 99.99% F1 score in loop closure detection. In pose estimation, it achieved a root mean square error (RMSE) of 0.836 meters or less for position and 0.195 degrees or less for heading. Furthermore, a time analysis on both a general PC and an embedded device confirmed the real-time capability of the proposed method, with an average pose estimation time of 21.70 milliseconds on the embedded device, demonstrating its feasibility for real-time localization in low-power environments.