The ALPHA-g experiment at CERN aims to perform the first-ever direct measurement of the effect of gravity on antimatter, determining its weight to within 1\% precision. This measurement requires an accurate prediction of the vertical position of annihilations within the detector. In this work, we developed a PointNet-like architecture to train a deep learning model to predict this successfully. Our model outperforms the standard approach to annihilation position reconstruction, providing twice the resolution while maintaining a similarly low bias. This work may also offer insights for similar efforts applying deep learning to experiments that require high resolution and low bias.