Soil moisture is a key limiting factor for mung bean yield, and rapid acquisition of its field-scale spatial distribution is essential for precision irrigation. Using UAV multispectral imagery at 30 m and 50 m flight altitudes, this study independently constructed Random Forest (RF) and Extreme Gradient Boosting (XGBoost) inversion models for the seedling, branching, flowering, and maturity stages. Model accuracy was evaluated via nested cross-validation, and decision mechanisms were interpreted using SHAP analysis. The results showed: (1) Inversion accuracy exhibited a unimodal trend across growth stages. At the seedling stage, the optimal model for the 0–20 cm layer was 50 m XGBoost (R² = 0.674), and for 20–40 cm was 30 m RF (R² = 0.709). At the branching stage, the 0–20 cm optimum was 50 m RF (R² = 0.860), and the 20–40 cm optimum was 50 m XGBoost (R² = 0.768). At the flowering stage, 30 m XGBoost was optimal for both 0–20 cm (R² = 0.887) and 20–40 cm (R² = 0.906). At the maturity stage, the 0–20 cm optimum was 50 m XGBoost (R² = 0.838), and the 20–40 cm optimum was 30 m XGBoost (R² = 0.654). (2) In full-growth-stage integrated modeling, RF achieved the highest accuracy (0–20 cm: 50 m, R² = 0.776; 20–40 cm: 30 m, R² = 0.935). (3) SHAP analysis revealed distinct feature utilization strategies between algorithms. For the 0–20 cm layer, OSAVI was the dominant factor. For the 20–40 cm layer, XGBoost exhibited an extreme feature-focus pattern (CIRE 53.72%), whereas RF showed a diversified feature distribution (NDWI 40.41%, CIRE 26.34%, GCI 23.3%). In summary, this study proposes a synergistic optimization strategy of growth stage × flight altitude × algorithm for soil moisture monitoring in mung bean, providing an explainable artificial intelligence solution for precision water management in leguminous crops using UAV remote sensing.