Our goal is to develop an efficient contact detection algorithm for large-scale GPU-based simulation of non-convex objects. Current GPU-based simulators such as IsaacGym and Brax must trade-off speed with fidelity, generality, or both when simulating non-convex objects. Their main issue lies in contact detection (CD): existing CD algorithms, such as Gilbert-Johnson-Keerthi (GJK), must trade off their computational speed with accuracy which becomes expensive as the number of collisions among non-convex objects increases. We propose a data-driven approach for CD, whose accuracy depends only on the quality and quantity of offline dataset rather than online computation time. Unlike GJK, our method inherently has a uniform computational flow, which facilitates efficient GPU usage based on advanced compilers such as XLA (Accelerated Linear Algebra). Further, we offer a data-efficient solution by learning the patterns of colliding local crop object shapes, rather than global object shapes which are harder to learn. We demonstrate our approach improves the efficiency of existing CD methods by a factor of 5-10 for non-convex objects with comparable accuracy. Using the previous work on contact resolution for a neural-network-based contact detector, we integrate our CD algorithm into the open-source GPU-based simulator, Brax, and show that we can improve the efficiency over IsaacGym and generality over standard Brax. We highly recommend the videos of our simulator included in the supplementary materials.