This paper presents a novel two-stage machine learning algorithm designed for total electron content forecasting. In the first stage, dimensionality reduction of the original TEC time series is performed using a standard fully-connected autoencoder. This process extracts compressed latent representations that encapsulate the essential temporal patterns and dependencies. In the second stage, these latent features are integrated with a set of external parameters known to influence ionospheric conditions: the critical frequency of the F2 layer (foF2), indices of solar (F10.7) and geomagnetic (Kp) activity, and temporal descriptors (seasonal and diurnal information). The resulting enriched feature set is used to train and evaluate several classical machine learning algorithms. Comparative analysis reveals that the CatBoost algorithm demonstrates superior predictive accuracy on the test dataset, outperforming other models as validated by Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics. The proposed method provides a robust and effective framework for TEC prediction, successfully leveraging the strengths of neural network-based feature extraction and the power of modern ensemble learning techniques.