The industrial metallization of Si solar cells predominantly relies on screen printing, with silver as the preferred electrode material. However, the design of commercial screens often leads to suboptimal silver usage and increased electrical resistance due to print-related inhomogeneities like mesh marks, constrictions and spreading. Real-time monitoring of quality parameters during production has thus become increasingly critical. Current inline optical quality control systems usually only include 2D visualizations of the printed layout, which limits their effectiveness in quality control. Options that allow 3D measurements are usually slow, expensive, and therefore not worth considering in most cases. This research focuses on the development of a model that can estimate the three-dimensional shape of printed contact fingers from a single 2D image without the need of additional hardware using deep learning. Furthermore, a workflow for the generation of training data, which involves the creation of image pairs from a 2D microscope and a 3D confocal laser scanning microscope (CLSM) to accurately represent solar cell fingers, is presented. After model training, the predicted height maps are compared with the ground truth height maps, and the robustness of the model with respect to a paste variation and screen parameter variation is examined. The results confirm the feasibility and reliability of deep learning-based 3D shape estimation, extending its applicability to new, previously unseen data from screen-printed contact fingers. With a structural similarity index (SSIM) score of 0.76, a strong correlation between the estimated and ground truth height maps is established. In summary, our deep learning-based approach for height map estimation offers an effective and reliable solution for fast inline detection and analysis of the cross-sectional area of the printed contact fingers.