Due to dynamic variations such as changing payload, aerodynamic disturbances, and varying platforms, a robust solution for quadrotor trajectory tracking remains challenging. To address these challenges, we present a deep reinforcement learning (DRL) framework that achieves physical dynamics invariance by directly optimizing force/torque inputs, eliminating the need for traditional intermediate control layers. Our architecture integrates a temporal trajectory encoder, which processes finite-horizon reference positions/velocities, with a latent dynamics encoder trained on historical state-action pairs to model platform-specific characteristics. Additionally, we introduce scale-aware dynamics randomization parameterized by the quadrotor's arm length, enabling our approach to maintain stability across drones spanning from 30g to 2.1kg and outperform other DRL baselines by 85% in tracking accuracy. Extensive real-world validation of our approach on the Crazyflie 2.1 quadrotor, encompassing over 200 flights, demonstrates robust adaptation to wind, ground effects, and swinging payloads while achieving less than 0.05m RMSE at speeds up to 2.0 m/s. This work introduces a universal quadrotor control paradigm that compensates for dynamic discrepancies across varied conditions and scales, paving the way for more resilient aerial systems.