Light particles with feeble interactions to the Standard Model have gathered theoretical and experimental interest. Beam-dump experiments rely on the high intensity of incoming beams to study particles with very small production rates, but might suffer from the limited detector resolution. In this work we use machine learning to explore the possibility to reconstruct the properties of an axion-like particle, in particular its mass and lifetime, at beam-dump experiments. We use a simulation-based inference approach built on conditional invertible neural networks to approximate the posterior probability of the model parameters for a given set of events. We find that for realistic angular and energy resolution, our neural network significantly outperforms parameter reconstruction from conventional high-level variables while at the same time providing reliable uncertainty estimates. The central point here is that our inference capability will depend on the specific detector design under consideration. One of the key advantages of this approach is that the neural network can quickly be re-trained for different detector properties, making it an ideal framework for optimizing experimental design.