The performance of covariance-based DoA estimation methods is limited in practice, particularly in the low signal-To-noise ratio (SNR) regime, due to the finite number of observations. In this work, we approach the direction-of-Arrival (DoA) estimation in the presence of extreme noise from the Machine Learning (ML) perspective using Deep Learning (DL). First, we derive a relation between the covariance matrix and its sample estimate formulating the problem as a manifold learning task. Next, we train a denoising autoencoder (DAE) that predicts a Hermitian matrix, which is subsequently used for the DoA estimation. Experimental results demonstrate significant performance gains in terms of the root-mean-squared error (RMSE) in the low-SNR regime by using popular covariance-based DoA estimators. Nevertheless, the proposed method runs independent of the DoA estimator, opening up new possibilities for the testing of other methods as well. We believe that the proposed approach has several applications, ranging from wireless array sensors to microphones and transducers used in ultrasound imaging, where the operating environments are characterized by extreme noise.