Groundwater depletion is arguably one of humanity's greatest sustainability challenges of the 21st century. With Sustainable Development Goals only a decade away, water authorities around the world are in the urgent need for concrete and targeted measures to ensure that communities adhere to groundwater management policies as rapidly and as effectively as possible. In this paper, we combine computational social science, groundwater modelling and empirical data from the World Values Survey to generate future ensembles of hydro-social trajectories under alternative courses of management and social action or inaction. Our simulations shed new light on the role that cultural values can play in shaping the societal trajectories and norms that emerge when resources are either allocated or not sufficiently allocated to monitor compliance, issue fines, engage community leaders, and deter rule-breakers. This study presents a new approach to explore and evaluate the capacity of existing and future management actions to steer groundwater systems towards sustainable trajectories, to forecast the celerity and timing of social transformations at the inter-decadal scale, and to help nations identify the most pertinent management options under institutional, political, social, and/or cultural constraints. The methods presented here are broadly applicable to support strategic decisions that rely on the monitoring, enforcement, and compliance of environmental regulations.