Time Projection Chambers (TPCs) are versatile detectors that reconstruct charged-particle tracks in an ionizing medium, enabling sensitive measurements across a wide range of nuclear physics experiments. We explore sparse convolutional networks for representation learning on TPC data, finding that a sparse ResNet architecture, even with randomly set weights, provides useful structured vector embeddings of events. Pre-training this architecture on a simple physics-motivated binary classification task further improves the embedding quality. Using data from the GAseous Detector with GErmanium Tagging (GADGET) II TPC, a detector optimized for measuring low-energy $β$-delayed particle decays, we represent raw pad-level signals as sparse tensors, train Minkowski Engine ResNet models, and probe the resulting event-level embeddings which reveal rich event structure. As a cross-detector test, we embed data from the Active-Target TPC (AT-TPC) -- a detector designed for nuclear reaction studies in inverse kinematics -- using the same encoder. We find that even an untrained sparse ResNet model provides useful embeddings of AT-TPC data, and we observe improvements when the model is trained on GADGET data. Together, these results highlight the potential of sparse convolutional techniques as a general tool for representation learning in diverse TPC experiments.