This work presents a date-driven user localization framework for single-site massive Multiple-Input-Multiple-Output (MIMO) systems. The framework is trained on a geo-tagged Channel State Information (CSI) dataset. Unlike the state-of-the-art Convolutional Neural Network (CNN) models, which require large training datasets to perform well, our method is specifically designed to operate with small-scale training datasets. This makes our approach more practical for real-world scenarios, where collecting a large amount of data can be challenging. Our proposed FC-AE-GPR framework combines two components: a Fully-Connected Auto-Encoder (FC-AE) and a Gaussian Process Regression (GPR) model. Our results show that the GPR model outperforms the CNN model when presented with small training datasets. However, the training complexity of GPR models can become an issue when the input sample size is large. To address this, we propose using the FC-AE to reduce the sample size by encoding the CSI before training the GPR model. Although the FC-AE model may require a larger training dataset initially, we demonstrate that the FC-AE is scenario independent. This means that it can be utilized in new and unseen scenarios without prior retraining. Therefore, adapting the FC-AE-GPR model to a new scenario requires only retraining the GPR model with a small training dataset.