Quadrotors hold significant promise for several applications such as agriculture, search and rescue, and infrastructure inspection. Achieving autonomous operation requires systems to navigate safely through complex and unfamiliar environments. This level of autonomy is particularly challenging due to the complexity of such environments and the need for real-time decision making especially for platforms constrained by size, weight, and power (SWaP), which limits flight time and precludes the use of bulky sensors like Light Detection and Ranging (LiDAR) for mapping. Furthermore, computing globally optimal, collision-free paths and translating them into time-optimized, safe trajectories in real time adds significant computational complexity. To address these challenges, we present a fully onboard, real-time navigation system that relies solely on lightweight onboard sensors. Our system constructs a dense 3D map of the environment using a novel visual depth estimation approach that fuses stereo and monocular learning-based depth, yielding longer-range, denser, and less noisy depth maps than conventional stereo methods. Building on this map, we introduce a novel planning and trajectory generation framework capable of rapidly computing time-optimal global trajectories. As the map is incrementally updated with new depth information, our system continuously refines the trajectory to maintain safety and optimality. Both our planner and trajectory generator outperforms state-of-the-art methods in terms of computational efficiency and guarantee obstacle-free trajectories. We validate our system through robust autonomous flight experiments in diverse indoor and outdoor environments, demonstrating its effectiveness for safe navigation in previously unknown settings.