Characteristics of the early current quench (CQ) time in mitigated disruptions are studied for a full-current (5.5 MA) scenario in the JT-60SA superconducting tokamak. Self-consistent evolution of the plasma temperature and current density profiles during the early CQ phase before the plasma moves vertically is simulated using the axisymmetric disruption code INDEX for given impurity source profiles. It is shown that the hollow (flat) impurity density profiles peaks (flattens) the current density, and it causes a temporal change in the internal inductance in this phase. However the resultant CQ time is found to be insensitive to the impurity source profile for the same assimilated quantity. The simulation results are interpreted by the L/R model including the temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates. This results will improve the accuracy to estimate the amount of impurity assimilated into plasma from the observed CQ rate in the massive gas injection (MGI) experiment planned in JT-60SA. The accessible range in which the CQ time can be scanned as well as the electron densities to suppress runaway electrons is also shown for different injected amounts of neon, argon, and their deuterium mixture under the limitation of the MGI gas amount. Mitigated disruptions in JT-60SA typically lead to the CQ time shorter than the vessel wall time, which is expected to produce relevant contributions to disruption mitigation in ITER and future reactors.