The cellular internet-of-things wireless network is a promising solution to provide massive connectivity for machine- type devices. However, designing grant-free random access (GF- RA) protocols to manage such connections is challenging, since they must operate in interference-aware scenarios with sporadic device activation patterns and a shortage of mutually orthogonal resources. Supervised machine learning models have provided efficient solutions for activity detection, non-coherent data detection, and non-orthogonal preamble design in scenarios with massive connectivity. Considering these promising results, in this paper, we develop two deep learning (DL) sparse support recovery algorithms to detect active devices in mMTC random access. The DL algorithms, developed to deploy GF-RA protocols, are based on the deep multilayer perceptron and the convolutional neural network models. Unlike previous works, we investigate the impact of the type of sequences for preamble design on the activity detection accuracy. Our results reveal that preambles based on the Zadoff-Chu sequences, which present good correlation properties, achieve better activity detection accuracy with the proposed algorithms than random sequences. Besides, we demonstrate that our DL algorithms achieve activity detection accuracy comparable to state-of-the-art techniques with extremely low computational complexity.