In recent years, millimeter wave (mmWave) massive MIMO systems have emerged as a promising solution to meet the increasing demand for high data rates and spectral efficiency in wireless communications. One of the primary challenges associated with these systems is the design of effective hybrid precoders, which have traditionally been constrained by channel training overheads and hardware limitations. This paper introduces a novel approach to tackle this challenge by harnessing the power of deep learning. Specifically, we employ the publicly available DeepMIMO dataset—a rich dataset that simulates realistic channel conditions—to train a deep neural network architecture aimed at optimizing the hybrid precoding process. Our approach focuses on directly designing the hybrid precoders/combiners to maximize the system’s achievable rate while minimizing the channel training overhead. Notably, our methodology jointly optimizes the design of RF beamforming and combining vectors along with compressive channel sensing vectors, thereby enhancing system performance. Preliminary results indicate that our deep learning-based method significantly outperforms traditional techniques in terms of spectral efficiency and robustness under various conditions. This study underscores the potential of leveraging machine learning tools for improving mmWave massive MIMO system design and paves the way for further research in this direction.