This paper presents a novel framework for robust 3D object detection from point clouds via cross-modal hallucination. Our proposed approach is agnostic to either hallucination direction between LiDAR and 4D radar. We introduce multiple alignments on both spatial and feature levels to achieve simultaneous backbone refinement and hallucination generation. Specifically, spatial alignment is proposed to deal with the geometry discrepancy for better instance matching between LiDAR and radar. The feature alignment step further bridges the intrinsic attribute gap between the sensing modalities and stabilizes the training. The trained object detection models can deal with difficult detection cases better, even though only single-modal data is used as the input during the inference stage. Extensive experiments on the View-of-Delft (VoD) dataset show that our proposed method outperforms the state-of-the-art (SOTA) methods for both radar and LiDAR object detection while maintaining competitive efficiency in runtime. Code is available at https://github.com/DJNing/See_beyond_seeing.