The two-dimensional electron system found between LaAlO3 and SrTiO3 hosts a variety of physical phenomena that can be tuned through external stimuli. This allows for electronic devices controlling magnetism, spin-orbit coupling, and superconductivity. Controlling the electron density by varying donor concentrations and using electrostatic gating are convenient handles to modify the electronic properties, but the impact on the microscopic scale, particularly of the former, remains underexplored. Here, we image the current distribution at 4.2 K in amorphous-LaAlO3/SrTiO3 using scanning superconducting-quantum-interference-device microscopy while changing the carrier density in situ using electrostatic gating and oxygen annealing. We show how potential disorder affects the current and how homogeneous 2D flow evolves into several parallel conducting channels when approaching the metal-to-insulator transition. We link this to ferroelastic domains and oxygen vacancies. This has important consequences for micro- and nanoscale devices with low carrier density and fundamental studies on quantum effects in oxides.