Navigating humanoid robots through dynamic, non-convex environments requires tightly coupling onboard perception with footstep planning and dynamic locomotion control. Existing methods frequently discard complex free space through simplified convex obstacle bounds and fail to account for real-time dynamic occupancy predictions. This paper presents a real-time framework for humanoid navigation that directly constructs spatio-temporal safe corridors from LiDAR-based particle representations and couples them with Linear Inverted Pendulum (LIP)-based planning and Whole Body Control (WBC) to enable navigation around and within moving non-convex structures without restrictive geometric assumptions. Simulations on the Digit humanoid yield a 96% success rate in navigating around and inside moving non-convex obstacles in a 24 by 24 m^2 arena. Ablation studies confirm that the proposed iterative polytope generation significantly outperforms single-iteration baselines in narrow corridors, while evaluations demonstrate robustness to clutter, sensor noise, control delays, and force perturbations.

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