A novel time-efficient framework is proposed for improving the robustness of a broadband multiple-input multiple-output (MIMO) system against unknown interference under rapidly-varying channels. A mean-squared error (MSE) minimization problem is formulated by optimizing the beamformers employed. Since the unknown interference statistics are the premise for solving the formulated problem, an interference statistics tracking (IST) module is first designed. The IST module exploits both the time- and spatial-domain correlations of the interference-plus-noise (IPN) covariance for the future predictions with data training. Compared to the conventional signal-free space sampling approach, the IST module can realize zero-pilot and low-latency estimation. Subsequently, an interference-resistant hybrid beamforming (IR-HBF) module is presented, which incorporates both the prior knowledge of the theoretical optimization method as well as the data-fed training. Taking advantage of the interpretable network structure, the IR-HBF module enables the simplified mapping from the interference statistics to the beamforming weights. The simulations are executed in high-mobility scenarios, where the numerical results unveil that: 1) the proposed IST module attains promising prediction accuracy compared to the conventional counterparts under different snapshot sampling errors; and 2) the proposed IR-HBF module achieves lower MSE with significantly reduced computational complexity.