Describing the nanoscale charge carrier transport at surfaces and interfaces is fundamental for designing high-performance optoelectronic devices. To achieve this, we employ time- and angle-resolved photoelectron spectroscopy with ultraviolet pump and extreme ultraviolet probe pulses. The resulting high surface sensitivity reveals an ultrafast carrier population decay associated with surface-to-bulk transport, which was tracked with a sub-nanometer spatial resolution normal to the surface, and on a femtosecond time scale, in the case of the inorganic CsPbBr₃ lead halide perovskite. The decay time exhibits a pronounced carrier density dependence, which is attributed via modeling to enhanced diffusive transport and concurrent recombination. The transport is found to approach an ordinary diffusive regime, limited by electron-hole scattering, at the highest excitation fluences. This approach constitutes an important milestone in our capability to probe hot-carrier transport at solid interfaces with sub-nanometer resolution in a theoretically and experimentally challenging, yet technologically relevant, high-carrier-density regime.