Although neural radiance fields (NeRFs) have achieved triumphs in image novel view synthesis (NVS), LiDAR NVS remains largely unexplored. Previous LiDAR NVS methods employ a simple shift from image NVS methods while ignoring the dynamic nature and the large-scale reconstruction problem of LiDAR point clouds. In light of this, we propose LiDAR4D, a differentiable LiDAR-only framework for novel space-time LiDAR view synthesis. In consideration of the sparsity and large-scale characteristics, we design a 4D hybrid representation combined with multi-planar and grid features to achieve effective reconstruction in a coarse-to-fine manner. Furthermore, we introduce geometric constraints derived from point clouds to improve temporal consistency. For the realistic synthesis of LiDAR point clouds, we incorporate the global optimization of ray-drop probability to preserve cross-region patterns. Extensive experiments on KITTI-360 and NuScenes datasets demonstrate the superiority of our method in accomplishing geometry-aware and time-consistent dynamic reconstruction.