In this paper, we explore the use of machine learning methods as an efficient alternative to correlation in performing packet detection. Targeting satellite-based massive machine type communications and internet of things scenarios, our focus is on a common channel shared among a large number of terminals via a fully asynchronous ALOHA protocol to attempt delivery of short data packets. In this setup, we test the performance of two algorithms, neural networks and random forest, which are shown to provide substantial improvements over {traditional} techniques. Excellent performance is demonstrated in terms of detection and false alarm probability also in the presence of collisions among user transmissions. The ability of machine learning to extract further information from incoming signals is also studied, discussing the possibility to classify detected preambles based on the level of interference they undergo.