The nucleation and subsequent growth of the reversed magnetic domain at a finite temperature are stochastic processes, which are often analyzed using an ensemble of magnetic elements. In this study, we investigate the stochastics of magnetization reversal in multiple trials for the sole magnetic domain. Specifically, we utilize the robust magnetic domain structure formed in a dual-exchange-biased Pt/Co/Au/Cr2O3/Pt thin film. Our investigation encompasses the latency of reversed domain nucleation and the subsequent domain wall motion based on time-lapse magnetic domain observations. The time evolution of the magnetic domain is observed after applying a pulsed magnetic field superimposed on a DC field. Magnetization reversal is triggered by the nucleation of a small embryo with finite latency, followed by domain wall propagation. The nucleation probability of the embryo increases exponentially with the DC field, thus indicating that the nucleation process obeys the Poisson process. An analysis of the relaxation time for nucleation provides a suitable expression for the energy barrier. The nucleated domain wall propagates with temporal stops, thus indicating creep motion. The temperature dependence of the relaxation time and domain wall creep motion reveal that the magnetic anisotropy in the antiferromagnetic layer significantly affect both the energy barrier for nucleation and the depinning potential of domain wall propagation. This study provides comprehensive understanding into the coercivity mechanism and contributes to the thermal stability of magnetic/spintronic devices.