UAV-based free-space optical (UAV–FSO) communication provides high-rate airborne links for future sixth-generation (6G) and non-terrestrial networks. Reliable initial beam alignment is challenging because UAV motion, pointing disturbances, and optical-channel variations jointly affect whether the received power can reach the acquisition threshold and remain available for protocol confirmation. In practical UAV–FSO scenarios, position-estimation errors, wind-induced drift, platform vibration, transmit-side pointing jitter and turbulence-related atmospheric fading appear as transverse line-of-sight uncertainty and pointing error. Therefore, initial link establishment should be treated as an online optical beam-alignment decision problem under evolving uncertainty rather than a fixed geometric scanning problem. This paper proposes PAME-Net, a physics-aware multi-stream expert framework for UAV–FSO beam alignment. PAME-Net describes optical disturbances and estimation uncertainty using covariance, residual history, Kalman-filter state estimates, and task-stage information. Thesecues guide adaptive pointing, beam-divergence control, scan-region allocation, and stage switching. A multi-stream encoder preserves the physical semantics of these cues, while an expert-decoupled multi-head module separates drift compensation, uncertainty-aware scan control, and stage switching. A two-stage execution mechanism combines rapid blind-shot pointing with covariance-guided scan-assisted alignment, and physics-consistent sample enrichment improves training robustness. In the strong-wind scenario with large position-estimation-induced transverse pointing uncertainty, PAME-Net achieves a 97.0% alignment success rate within 1.0 s and reduces the mean successful alignment time to 0.548 s. It also maintains stable performance under increasing uncertainty and continuous-dwell requirements.