Astrometric lensing has recently emerged as a promising avenue for characterizing the population of dark matter clumps---subhalos---in our Galaxy. Leveraging recent advances in simulation-based inference and neural network architectures, we introduce a novel method to look for global dark matter-induced lensing signatures in astrometric datasets. Our method shows significantly greater sensitivity to a cold dark matter population compared to existing approaches, establishing machine learning as a powerful tool for characterizing dark matter using astrometric data.