This study addressed the intricate interplay between meteorological droughts and groundwater level fluctuations in the vicinity of Mount Uludag in Bursa, Turkey. To achieve this, an exhaustive analysis encompassing monthly precipitation records and groundwater level data sourced from three meteorological stations and eight groundwater observation points spanning the period from 2007 to 2018 was performed. Subsequently, this study employed the Standard Precipitation Index (SPI) and Standard Groundwater Level (SGL) metrics, meticulously calculating the temporal extents of drought events for each respective time series. Following this, a judicious application of both the Thiessen and Support Vector Machine (SVM) methodologies was undertaken to ascertain the optimal groundwater observation wells and their corresponding SGL durations, aligning them with SPI durations tied to the selected meteorological stations. The SVM technique, in particular, excelled in the identification of the most pertinent observation wells. Additionally, the Elman Neural Network (ENN) and its optimized version through the Firefly Algorithm (ENN-FA), demonstrated their prowess in accurately predicting SPI durations based on SGL durations. The results were favorable, as evidenced by the commendable performance metrics of the Normalized Root Mean Square Error (NRMSE), the Nash–Sutcliffe Efficiency (NSE), the product of the coefficient of determination and the slope of the regression line (bR2), and the Kling–Gupta Efficiency (KGE). Consequently, the favorable simulation results were construed as evidence supporting the presence of a discernible association between SGL and the duration of the SPI. As we substantiate the concordance between the temporal extent of meteorological droughts and the perturbations in groundwater levels, this unmistakably underscores the fact that the historical fluctuations in groundwater levels within the region were predominantly attributable to climatic influences, rather than being instigated by anthropogenic activities. Nevertheless, it is imperative to underscore that this revelation should not be misconstrued as an endorsement of future heedless exploitation of groundwater resources.