Evidential occupancy grid maps (OGMs) are a popular representation of the environment of automated vehicles. Inverse sensor models (ISMs) are used to compute OGMs from sensor data such as lidar point clouds. Geometric ISMs show a limited performance when estimating states in unobserved but inferable areas and have difficulties dealing with ambiguous input. Deep learning-based ISMs face the challenge of limited training data and they often cannot handle uncertainty quantification yet. We propose a deep learning-based framework for learning an OGM algorithm which is both capable of quantifying first- and second-order uncertainty and which does not rely on manually labeled data. Results on synthetic and on real-world data show superiority over other approaches. Source code and datasets are available at https://github.com/ika-rwth-aachen/EviLOG