High-mobility uncrewed aerial vehicle (UAV) communications in low-altitude wireless networks (LAWN) demand reliable beamforming, while conventional feedback-based schemes suffer from excessive overhead and severe misalignment under rapid trajectory variations. To address this challenge, this paper proposes an SSB-based sensing-assisted predictive robust beamforming framework that replaces explicit channel state information (CSI) feedback with sensing-driven state estimation and uncertainty-aware optimization. Leveraging the periodic 'always-on' synchronization signal block (SSB), a hierarchical sensing algorithm tailored for hybrid digital-analog uniform planar arrays is developed, combining 2D range-velocity profiling and augmented beamspace multiple signal classification (MUSIC). By integrating a locally-focused analog receive beamformer, the proposed sensing design can ensure energy accumulates across different radio-frequency (RF) chains while resolving angular ambiguity. An extended Kalman filter (EKF) is further employed to track UAV states between sparse synchronization-signal (SS) bursts, and a covariance correction is introduced to characterize maneuver-induced prediction uncertainties. Based on the derived statistical distributions of range and angular parameters, the communication channel is modeled through predictive correlation matrices rather than instantaneous CSI, leading to a multi-user robust beamforming formulation that maximizes average network sum-rate under uncertainty. The resulting nonconvex problem is efficiently solved via successive convex approximation and alternating minimization. Simulation results demonstrate that the proposed framework significantly enhances spectral efficiency and link stability compared with feedback-based beamforming and non-robust beamforming design, particularly in high-mobility and large-SSB-interval scenarios.