Grant-free non-orthogonal multiple access (NOMA) is considered as one of the supporting technology for massive connectivity for future networks. In the grant-free NOMA systems with a massive number of users, user activity detection is of great importance. Existing multi-user detection (MUD) techniques rely on complicated update steps which may cause latency in signal detection. In this paper, we propose a generative neural network-based MUD (GenMUD) framework to utilize low-complexity neural networks, which are trained to reconstruct signals in a small fixed number of steps. By exploiting the uncorrelated user behaviours, we design a network architecture to achieve higher recovery accuracy with a low computational cost. Experimental results show significant performance gains in detection accuracy compared to conventional solutions under different channel conditions and user sparsity levels. We also provide a sparsity estimator through extensive experiments. Simulation results of the sparsity estimator showed high estimation accuracy, strong robustness to channel variations and neglectable impact on support detection accuracy.