Accurate assessment of snowpack volumetric liquid water content and bulk density is essential for understanding snow hydrology, avalanche risk management, and monitoring cryosphere changes. This study presents a novel dual-parameter inversion framework that integrates synthetic electromagnetic modelling, dimensionality reduction, and machine learning algorithms to extract relative permittivity and log-resistivity from ground-penetrating radar (GPR) data. Traditional snowpack measurements are invasive, labor-intensive, and limited to point observations. To overcome these limitations, we developed a non-invasive, scalable, and data-driven framework that uses synthetic GPR datasets representing diverse snowpack conditions with variable moisture and density profiles. Synthetic 1D time series reflections (A-scans) are generated using finite-difference time-domain simulations in the state-of-the-art electromagnetic simulator gprMax. Principal component analysis (PCA) is applied to compress each A-scan while preserving key features, which significantly improved and enhanced the model training efficiency. Four machine learning models, including random forest, neural network, support vector machine, and eXtreme gradient boosting, are trained on PCA-reduced features. Among these, the neural network model achieved the best performance, with R-2>0.97 for permittivity and R-2>0.92 for resistivity. Gaussian noise (signal-to-noise ratio of 6 dB) is introduced to the synthetic data, and then targeted domain adaptation is employed to enhance generalization to field data. The framework is validated on two contrasting GPR transects in the Altay Mountains of the Chinese mainland, representing moist (T750) and wet (G125) snowpack conditions. The neural network model predictions are most consistent with the GPR derived estimates, Snowfork measurements, and snow pit data, achieving volumetric liquid water content deviation of <= 1.5% and bulk density error within the range of 30-84 kg m(-3). The results demonstrate that machine learning-based inversion, supported by realistic simulations and data augmentation enables scalable, non-invasive snowpack characterization with significant applications in hydrological forecasting, snow monitoring, and water resource management.