East African March–May rainfall (MAM) remains difficult to predict despite its importance for agriculture, water resources, and disaster preparedness. This study identifies pre-season physical drivers of MAM rainfall and tests their value for probabilistic seasonal prediction. Predictor basins were derived from December and January sea surface temperature (SST), 2 m air temperature (T2), and sea-level pressure (SLP) anomalies relative to 1991–2020, using correlations with the leading mode of East African MAM rainfall and subsequent SHAP-based feature selection. The selected basin-derived indices were applied in Random Forest (RF) and Extreme Gradient Boosting (XGB) models. The dominant predictors appear to be the southern Indian Ocean T2 tendency, Australian and Eurasian T2 gradients, South Pacific and Antarctic T2 signals, Atlantic Niño tendency, and the Euro–African SLP gradient. T2-related predictors dominate both the January and December initialisations, showing that near-surface thermal gradients provide useful information in addition to SST memory. Walker-circulation diagnostics show that these drivers influence rainfall through pressure-gradient changes, tropical overturning, and upper-level wave-train development. For January initialisation, RF and XGB achieve spatially averaged Brier Skill Scores of 0.48 and 0.41, respectively, while the corresponding Area Under the Receiver Operating Characteristic Curve values amounting to 0.72 and 0.65. These results demonstrate that physically constrained machine learning provides promising probabilistic skill for East African MAM rainfall prediction.