Accurate forest height estimation is crucial for climate change monitoring and carbon cycle assessment. Synthetic Aperture Radar (SAR), particularly in multi-channel configurations, has provided support for a long time in 3D forest structure reconstruction through model-based techniques. More recently, data-driven approaches using Machine Learning (ML) and Deep Learning (DL) have enabled new opportunities for forest parameter retrieval. This paper introduces FGump, a forest height estimation framework by gradient boosting using multi-channel SAR processing with LiDAR profiles as Ground Truth(GT). Unlike typical ML and DL approaches that require large datasets and complex architectures, FGump ensures a strong balance between accuracy and computational efficiency, using a limited set of hand-designed features and avoiding heavy preprocessing (e.g., calibration and/or quantization). Evaluated under both classification and regression paradigms, the proposed framework demonstrates that the regression formulation enables fine-grained, continuous estimations and avoids quantization artifacts by resulting in more precise measurements without rounding. Experimental results confirm that FGump outperforms State-of-the-Art (SOTA) AI-based and classical methods, achieving higher accuracy and significantly lower training and inference times, as demonstrated in our results.