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Influenza A outbreaks in Saudi Arabia exhibit different seasonal patterns, influenced by significant changes, including a near-total halt during the COVID-19 pandemic (2020-2021) and a substantial rebound, as evidenced by national surveillance data, until the end of 2023. Traditional time-series models rely on stationarity and stable seasonal patterns; however, these assumptions are significantly undermined by regime shifts. This study introduces a forecasting method that uses light gradient boost machine (LightGBM) regression, along with Seasonal-Trend decomposition using LOESS (STL), to better track influenza in changing contexts. The proposed method adapts to the evolving epidemiological dynamics shaped by policy and behavioral changes by decomposing the incidence series into long-term trends, stable annual seasonal components, and irregular residual fluctuations prior to nonlinear learning. Exploratory analysis supports strong winter seasonality, linear correlations with meteorological variables, and major structural disruptions linked to pandemic-related interventions. shows how standard SARIMAX and seasonal baseline models cannot be used across all epidemiological regimes. The hybrid model, when evaluated during the test window, shows strong out-of-sample performance, substantially outperforming the benchmark models (R ² = 0.831, MAE = 89.0). In-sample fitting throughout the study period indicates a high degree of representational capacity (R ² = 0.987). The framework is further extended to probabilistic forecasting via quantile regression, resulting in accurately calibrated 95% prediction intervals. The uncertainty in the predictions increases appropriately during periods of epidemiological disruption, highlighting the importance of uncertainty-aware prediction under structural change. The proposed STL-LightGBM architecture is a resilient and comprehensible instrument for monitoring influenza in post-pandemic contexts, facilitating early warning systems and expeditious public health decision-making in Saudi Arabia and analogous regions.