Recent high-resolution mm and sub-mm observations of molecular clouds suggest that rotationally supported disks around nascent protostars can reach sizes as large as ~100 au during the Class I stage. However, non-ideal MHD simulations using realistic initial conditions and magnetic diffusivities generally find that the material being accreted by the protostar-disk system has a specific angular momentum much lower than that of a large disk. Resolving this apparent disparity requires a more complete understanding of the accretion, removal, and redistribution of angular momentum in protostellar cores. To this end, we perform and analyze a 3D non-ideal MHD simulation of a collapsing protostellar core, covering the formation and early evolution of a protostellar accretion disk. We find that most of the angular momentum that is accreted from the surrounding pseudo-disk and envelope remains in the disk, due to the inability of protostellar outflows and magnetic braking in the disk to remove angular momentum efficiently. The accumulated angular momentum is then redistributed within the massive disk by gravitational instability, which causes the disk to spread until most of the disk becomes marginally unstable. As a result, large rotationally supported disks may form even when the material accreted by the disk has very low specific angular momentum.