This paper proposes a deep learning approach to channel sensing and downlink hybrid beamforming for massive multiple-input multiple-output systems operating in the time division duplex mode and employing either single-carrier or multicarrier transmission. The conventional precoding design involves a two-step process of first estimating the high-dimensional channel, then designing the precoders based on such estimate. This two-step process is, however, not necessarily optimal. This paper shows that by using a learning approach to design the analog sensing and the hybrid downlink precoders directly from the received pilots without the intermediate high-dimensional channel estimation, the overall system performance can be significantly improved. Training a neural network to design the analog and digital precoders simultaneously is, however, difficult. Further, such an approach is not generalizable to systems with different number of users. In this paper, we develop a simplified and generalizable approach that learns the uplink sensing matrix and downlink analog precoder using a deep neural network that decomposes on a per-user basis, then designs the digital precoder based on the estimated low-dimensional equivalent channel. Numerical comparisons show that the proposed methodology results in significantly less training overhead and leads to an architecture that generalizes to various system settings.