The study is to establish a progressive first-failure censoring step-stress partially accelerated life testing plan for Gompertz distribution. The distribution parameters and acceleration factor are estimated using maximum likelihood estimation (MLEs). Additionally, the estimators' asymptotic variance, confidence intervals, and covariance matrices are provided. To obtain the optimal stress change time for the step-stress partially accelerated life test, the asymptotic variance of the MLEs of the parameters is minimized. The results of the simulations are used to determine the precision of the MLEs for the parameters under consideration.