Full waveform (FW) LiDAR systems have proven their effectiveness to map forest biophysical variables in the last two decades, owing to their ability of measuring, with high accuracy, forest vertical structures. The Global Ecosystem Dynamics Investigation (GEDI) system on board the International Space Station (ISS) is the latest FW spaceborne LiDAR instrument for the continuous observation of Earth's forests. FW systems rely on very sophisticated pre-processing steps to generate a priori metrics in order to leverage their capabilities for the accurate estimation of the aforementioned forest characteristics. The ever-expanding volume of acquired GEDI data, which to date comprises more than 25 billion acquired unfiltered shots, and along with the pre-processed data, amounting to more than 90 TB of data, raises new challenges in terms of adapted preprocessing methods for the suitable exploitation of such a huge and complex amount of LiDAR data. To overcome the issues related to the generation of relevant metrics from GEDI data, we propose a new metric-free approach to estimate canopy dominant heights (Hdom) and wood volume (V) of Eucalyptus plantations over five different regions in Brazil. To avoid metric computation, we leverage deep learning techniques and, more in detail, convolutional neural networks with the aim to analyze the GEDI Level 1B geolocated waveforms. Performance comparisons were conducted between four convolutional neural network (CNN) variants using GEDI waveform data (either untouched, or subsetted) and a metric based Random Forest regressor (RF). Additionally, we tested if our framework can improve the generalization of the models to different distant regions. First, the models were trained using data from all the study regions. Cross validated results showed that the CNN based models compared well against their RF counterpart for both Hdom and V. The RMSE on the estimation of Hdom from the CNN based models varied between 1.54 and 1.94 m with a coefficient of determination (R2) between 0.86 and 0.91, while the RF model produced an accuracy on Hdom estimates of 1.45 m (R2 = 0.92). For V, CNN based estimations ranged from 27.76 to 33.33 m3.ha−1 (R2 between 0.82 and 0.88), while for RF, the RMSE was 27.61 m3.ha−1 (R2 = 0.88). Next, model generalization was assessed by means of a spatial transfer experiment. For Hdom, both the CNN and RF approaches showed similar performances to a global model, however, the CNN based approach showed higher variability on the estimation accuracy, and the variability was related to the forest structure between the trained and tested data (similar tree heights yield better accuracies). For the estimation of V, considering both approaches, the accuracy was dependent on the allometric relationship between Hdom and V in the training and testing regions while lower accuracies on V were obtained when the testing and training regions exhibited a different allometric relationship.