We consider super-critical accretion with angular momentum onto stellar-mass black holes as a possible mechanism for growing billion-solar-mass black holes from light seeds at early times. We use the radiatively inefficient "slim disk" solution-advective, optically thick flows that generalize the standard geometrically thin disk model-to show how mildly super-Eddington intermittent accretion may significantly ease the problem of assembling the first massive black holes when the universe was less than 0.8 Gyr old. Because of the low radiative efficiencies of slim disks around non-rotating as well as rapidly rotating black holes, the mass e-folding timescale in this regime is nearly independent of the spin parameter. The conditions that may lead to super-critical growth in the early universe are briefly discussed.