In the last 10 years, the demand for robot-based depalletization systems has constantly increased due to the growth of sectors such as logistics, storage, and supply chains. Since the scenarios are becoming more and more unstructured, characterized by unknown pallet layouts and stock-keeping unit shapes, the classical depalletization systems based on the knowledge of predefined positions within the pallet frame are going to be substituted by innovative and robust solutions based on 2D/3D vision and Deep Learning (DL) methods. In particular, the Convolutional Neural Networks (CNNs) are deep networks that have proven to be effective in processing 2D/3D images, for example in the automatic object detection task, and robust to the possible variability among the data. However, deep neural networks need a big amount of data to be trained. In this context, whenever deep networks are involved in object detection for supporting depalletization systems, the dataset collection represents one of the main bottlenecks during the commissioning phase. The present work aims at comparing different training strategies to customize an object detection model aiming at minimizing the number of images required for model fitting, while ensuring reliable and robust performances. Different approaches based on a CNN for object detection are proposed, evaluated, and compared in terms of the F1-score. The study was conducted considering different starting conditions in terms of the neural network’s weights, the datasets, and the training set sizes. The proposed approaches were evaluated on the detection of different kinds of paper boxes placed on an industrial pallet. The outcome of the work validates that the best strategy is based on fine-tuning of a CNN-based model already trained on the detection of paper boxes, with a median F1-score greater than $85.0\%$.