Autonomous systems often employ multiple LiDARs to leverage the integrated advantages, enhancing perception and robustness. The most critical prerequisite under this setting is the estimating the extrinsic between each LiDAR, i.e., calibration. Despite the exciting progress in multi-LiDAR calibration efforts, a universal, sensor-agnostic calibration method remains elusive. According to the coarse-to-fine framework, we first design a spherical descriptor TERRA for 3-DoF rotation initialization with no prior knowledge. To further optimize, we present JEEP for the joint estimation of extrinsic and pose, integrating geometric and motion information to overcome factors affecting the point cloud registration. Finally, the LiDAR poses optimized by the hierarchical optimization module are input to time synchronization module to produce the ultimate calibration results, including the time offset. To verify the effectiveness, we conduct extensive experiments on eight datasets, where 16 diverse types of LiDARs in total and dozens of calibration tasks are tested. In the challenging tasks, the calibration errors can still be controlled within 5cm and 1{\deg} with a high success rate.