In recent years On-Orbit Servicing and Active Debris Removal have assumed an increasing importance. In this context, accurate relative pose determination is essential to enable a safe and automated rendezvous between a servicing spacecraft and a client spacecraft that needs to be serviced. The use of machine learning to provide such information represents a cutting-edge technology. The aim of this work is to define a deep learning-based method that, by leveraging LiDAR-derived depth images, can provide a coarse but robust initial estimate of the attitude of a non-cooperative spacecraft. After developing a baseline Convolutional Neural Network for single-frame attitude estimation, the architecture is enhanced by integrating a recurrent module.