Tens of thousands of galaxy-galaxy strong lensing systems are expected to be discovered by the end of the decade. These will form a vast new dataset that can be used to probe subgalactic dark matter structures through its gravitational effects, which will in turn allow us to study the nature of dark matter at small length scales. This work shows how we can leverage machine learning to search through the data and identify which systems are most likely to contain dark matter substructure and thus can be studied in greater depth. We use a UNet, an image segmentation architecture, on a simulated strongly-lensed dataset with realistic sources (COSMOS galaxies), lenses (power-law elliptical profiles with multipoles and external shear), and noise. Our machine learning algorithm is able to quickly detect most substructure at high image resolution and subhalo concentration. At a false positive rate of $10\%$, we are able to identify systems with substructure at a true positive rate of $71\%$ for a subhalo mass range of $10^{9}\text{-}10^{9.5}\,M_\odot$. While recent detections are consistent with higher concentrations, we find that our algorithm fails at detecting subhalos with lower concentrations (expected from $\Lambda$CDM simulations).