Accurate estimation of soil organic matter (SOM) in saline semi-arid environments is essential for assessing soil fertility and supporting sustainable land management. This study investigates the potential of a single EnMAP hyperspectral image combined with machine learning, spectral pre-processing, and feature selection techniques for SOM prediction. Random Forest (RF) regression was employed alongside three feature selection methods: RF feature importance (RFFS), Competitive Adaptive Reweighted Sampling (CARS), and Recursive Feature Elimination (RFE). Several spectral pre-processing techniques, including first derivative (FD), second derivative, Savitzky–Golay (SG), standard normal variate (SNV), and absorbance transformation, were evaluated. Results indicate that models based on original reflectance achieved only moderate performance (PCCC = 0.547–0.617; R² = 0.295–0.354). In contrast, spectral transformations, particularly FD, significantly improved predictive accuracy. The best-performing model (FD-RFFS) achieved PCCC = 0.697 (p < 0.001), R² = 0.446, RMSE = 0.825, and MAE = 0.643, representing notable improvements over raw spectra. Feature selection further enhanced model robustness, with RFFS outperforming CARS and RFE. Analysis of selected wavelengths revealed consistent importance of spectral regions within the visible–NIR (418–801 nm) and SWIR-2 (2207–2445 nm) ranges, highlighting their sensitivity to SOM variability. These findings demonstrate that combining derivative-based pre-processing with RF-driven feature selection improves SOM estimation from hyperspectral data. The proposed framework provides an effective and operational approach for SOM mapping in saline semi-arid landscapes.