Automotive radar is a key component of sensing suites in autonomous driving (AD) and advanced driver-assist systems (ADAS). However, limited line-of-sight (LOS) significantly reduces radar efficiency in dense urban environments. Therefore, automotive radars need to extend their capabilities beyond LOS by localizing occluding and reflective surfaces and non-line-of-sight (NLOS) targets. This work addresses the NLOS target localization challenge by revisiting the NLOS radar signal propagation model and introducing a hybrid localization approach. The proposed approach first detects and localizes reflective surfaces, then identifies the LOS/NLOS propagation conditions, and finally localizes the target without prior scene knowledge, without using Doppler information, and without any auxiliary sensors. The proposed hybrid approach addresses the computational complexity challenge by integrating a physical radar electromagnetic wave propagation model with a deep neural network (DNN) to estimate occluding surface parameters. The efficiency of the proposed approach to localize the NLOS targets and to identify the NLOS/LOS propagation conditions is evaluated via simulations in a broad range of realistic automotive scenarios. Extending automotive radar sensing beyond LOS is expected to enhance the safety and reliability of autonomous and ADAS-equipped vehicles.