We propose ASCENT, a novel framework for tracking neurons in 3D fluorescence microscopy recordings without relying on manual track annotations. ASCENT leverages self-supervised contrastive learning to learn robust, discriminative embeddings from detected neuron candidates. At its core is a volume compression module that transforms full 3D volumetric data into an efficient 2D representation by iteratively projecting along the z-axis and integrating positional information. This compressed representation is processed by a deep encoder (e.g., ResNet or Vision Transformer) to yield robust feature vectors that capture both appearance and spatial relationships among neurons. Extensive experiments on both in-house and public datasets demonstrate that ASCENT achieves state-of-the-art tracking performance with fast inference speed while removing the need for costly manual labeling and heavy pre- and post-processing. Our results suggest that this approach provides a scalable solution for 3D neuron tracking and holds promise for applications such as inter-individual neuron identity matching and demixing overlapping cells.