Developing a reliable conceptual model is crucial for analyzing groundwater systems. An essential part of the aquifer conceptualization is the identification of the hydrological stresses that control the hydraulic head fluctuations. By effectively capturing and understanding these stresses, the propagation of potential errors and uncertainties through subsequent modeling steps can be minimized. This study aims to test data-driven models as screening models for conceptualizing a groundwater system. The case study is applied to the Grazer Feld Aquifer in southeast Austria. Time series models are applied to: (1) identify the stresses likely influencing the observed head fluctuations and their spatial variability; (2) identify locations where a lack of understanding of head fluctuations exists; and (3) discuss the limitations and opportunities associated with data-driven models to support system conceptualization. Time series models were created for 144 monitoring wells where sufficient head observations were available during the calibration period (2005–2015). A total of 576 models were developed, incorporating the combinations of stresses: recharge, river level, and a step trend. Following the model selection process, each model was categorized based on its performance and divided into four groups. At 88 sites, recharge and river level variations were identified as the primary controlling stresses influencing head fluctuations. The inclusion of the step trend was found to be necessary at five sites to accurately simulate heads due to dam construction. The application of data-driven models in this study enhanced the identification of key aquifer stresses, facilitating a more informed understanding of the groundwater system.