Optimum groundwater management is important for addressing the global challenges of water scarcity, especially in arid regions. This study demonstrates the application of synthetic data combined with seismic methods to quantify water volumes in a controlled sand pool environment, mimicking a subsurface aquifer. Utilizing seismic simulations, we employ the nodal discontinuous Galerkin method to generate data reflecting the propagation of seismic waves through a three-dimensional poroviscoelastic-viscoelastic medium. These data are then analyzed using fully connected neural networks optimized through hyperparameter tuning to predict the water volume from seismic signatures accurately. The approach incorporates Deep Evidential Regression, which quantifies two main types of uncertainties: aleatoric, resulting from measurement errors, and epistemic, resulting from inadequate model knowledge. This dual uncertainty quantification enhances the reliability and interpretability of the water volume predictions, providing a robust framework for groundwater monitoring. Our results indicate that the aleatoric uncertainties are nearly consistent but, epistemic uncertainties are large for higher values of water volume suggesting the possibility of adding more data for model improvement.