Fifth generation (5G) communication systems are expected to provide an ubiquitous solution for indoor positioning, and deep neural networks (DNNs) have been recently proposed for this purpose. However, DNN-based positioning solutions are in general very dependent on the training data. In this paper, an architecture for positioning based on wireless signals is proposed, namely the SAGE-Enhanced CEAP (SE-CEAP). The architecture considers firstly an enhancement of the acquired Channel State Information (CSI) data by means of a high-resolution parameter estimation (HRPE) method, namely the space-alternating generalized-expectation maximization (SAGE) algorithm, and secondly a specifically designed DNN for localization, namely the CNN-Enblock AI Positioning (CEAP). The provided results, considering a realistic 5G New Radio (NR) deployment in an indoor scenario, show that the proposed architecture outperforms other classical DNN-based localization approaches, not only in localization accuracy, but also in generalizability of the results, which is a common drawback of DNN-based solutions.