Fresh water availability is critical for ecosystems, agriculture, industry, and human communities. Anticipating drought conditions benefits from forecasting changes in terrestrial water storage (TWS), the total water stored on land across all compartments, including groundwater, rivers, glaciers, and soil moisture. While individual compartments, such as groundwater, are difficult to observe directly at large scales, TWS integrates their combined changes and can be measured globally through satellite gravimetry. Since 2002, the GRACE and GRACE Follow-On (GRACE-FO) missions have delivered monthly, global estimates of terrestrial water storage anomalies (TWSA), deviations from a long-term mean, making TWSA the most accessible large-scale indicator of hydrological change. Predicting TWSA is nonetheless challenging as it reflects processes operating at vastly different temporal and spatial scales. We present HiGNN-LSTM, a hierarchical graph neural network that represents the Earth across two spatial scales, coupled with an LSTM module to forecast global TWSA for up to six months ahead. As a proof of concept, we show that the hierarchical graph neural network can automatically generate meaningful input features for TWSA forecasting from ERA5 climate variables, without requiring manual predictor selection or lag-correlation analysis. Trained on a GRACE-like reconstruction of TWSA extending from 1979 to 2020, the model substantially reduces the one-month-lead RMSE relative to a seasonal climatology baseline (1.83 cm vs 3.70 cm) and consistently outperforms a ConvLSTM across the full six-month horizon. Skill over climatology shrinks at longer leads and is lost by six months, indicating that most of the gain concentrates at short leads. Evaluation against GRACE- and GRACE-FO-derived TWSA highlights the difficulty of transferring a model trained on reconstructed TWSA to satellite-derived observations.