As part of the U.S. National Spectrum Strategy, the 3.1−3.45 GHz band has been identified as a candidate for coexistence with commercial broadband access. The band currently supports defense radar systems with strict covertness and legacy constraints, which rules out cooperative methods for radar-communication system coexistence. This paper proposes a Machine Learning (ML)-assisted approach to detecting radar chirps in a non-cooperative spectrum-sharing environment. Inputs to the ML algorithm are beamforming errors observed during uplink training. We develop both supervised and unsupervised detection algorithms that operate without explicit channel estimation, spectrum sensing, or prior knowledge of radar parameters. Simulations demonstrate that the proposed ML algorithms provide significant improvements over a prior univariate detection benchmark. Specifically, supervised models achieve Area Under Curve scores below 1%, while the unsupervised OCSVM achieves approximately 3% AUC, highlighting the efficacy of multivariate decision functions in capturing complex temporal and spectral interference patterns. The numerical results illustrate the potential of ML techniques to facilitate robust non-cooperative spectrum sharing between radar and communication systems in dynamically changing environments.