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Following an earthquake, ground motion time series are needed to carry out site-specific nonlinear response history analysis. However, the number of currently available recording instruments is sparse; thus, the ground motion time series at uninstrumented sites must be estimated. Tamhidi et al. developed a Gaussian process regression (GPR) model to generate ground motion time series given a set of recorded ground motions surrounding the target site. This GPR model interpolates the observed ground motions’ Fourier Transform coefficients to generate the target site’s Fourier spectrum and the corresponding time series. The robustness of the optimized hyperparameter of the model depends on the surrounding observation density. In this study, we carried out sensitivity analysis and tuned the hyperparameter of the GPR model for various observation densities. The 2019 M7.1 Ridgecrest and 2020 M4.5 South El Monte earthquake data sets recorded by the Community Seismic Network and California Integrated Seismic Network in Southern California are used to demonstrate the process. To provide a tool to quantify the uncertainty of the generated motions, a methodology to develop realizations of ground motion time series is also incorporated. The results illustrate that the uncertainty of the generated motions is lower at longer periods. It is shown that the observation density in the proximity of the target site plays a vital role in both error and uncertainty reduction of the generated time series. To demonstrate the concept, the effect of additional observations from combined recording networks is investigated.