The forest stock volume (FSV) is one of the key indicators in forestry resource assessments on local, regional, and national scales. To date, scaling up in situ plot-scale measurements across landscapes is still a great challenge in the estimation of FSVs. In this study, Sentinel-2 imagery, the Google Earth Engine (GEE) cloud computing platform, three base station joint differential positioning technology (TBSJDPT), and three algorithms were used to build an FSV model for forests located in Hunan Province, southern China. The GEE cloud computing platform was used to extract the imagery variables from the Sentinel-2 imagery pixels. The TBSJDPT was put forward and used to provide high-precision positions of the sample plot data. The random forests (RF), support vector regression (SVR), and multiple linear regression (MLR) algorithms were used to estimate the FSV. For each pixel, 24 variables were extracted from the Sentinel-2 images taken in 2017 and 2018. The RF model performed the best in both the training phase (i.e., R2 = 0.91, RMSE = 35.13 m3 ha−1, n = 321) and in the test phase (i.e., R2 = 0.58, RMSE = 65.03 m3 ha−1, and n = 138). This model was followed by the SVR model (R2 = 0.54, RMSE = 65.60 m3 ha−1, n = 321 in training; R2 = 0.54, RMSE = 66.00 m3 ha−1, n = 138 in testing), which was slightly better than the MLR model (R2 = 0.38, RMSE = 75.74 m3 ha−1, and n = 321 in training; R2 = 0.49, RMSE = 70.22 m3 ha−1, and n = 138 in testing) in both the training phase and test phase. The best predictive band was Red-Edge 1 (B5), which performed well both in the machine learning methods and in the MLR method. The Blue band (B2), Green band (B3), Red band (B4), SWIR2 band (B12), and vegetation indices (TCW, NDVI_B5, and TCB) were used in the machine learning models, and only one vegetation index (MSI) was used in the MLR model. We mapped the FSV distribution in Hunan Province (3.50 × 108 m3) based on the RF model; it reached a total accuracy of 63.87% compared with the official forest report in 2017 (5.48 × 108 m3). The results from this study will help develop and improve satellite-based methods to estimate FSVs on local, regional and national scales.