Modern wireless networks must reliably support a wide array of connectivity demands, encompassing various user needs across diverse scenarios. Machine-Type Communication (mMTC) is pivotal in these networks, particularly given the challenges posed by massive connectivity and sporadic device activation patterns. Traditional grant-based random access (GB-RA) protocols face limitations due to constrained orthogonal preamble resources. In response, the adoption of grant-free random access (GF-RA) protocols offers a promising solution. This paper explores the application of supervised machine learning models to tackle activity detection issues in scenarios where nonorthogonal preamble design is considered. We introduce a datadriven algorithm specifically designed for user activity detection in Cell-Free Massive Multiple-Input Multiple-Output (CF-mMIMO) networks operating under GF-RA protocols. Additionally, this study presents a novel clustering strategy that simplifies and enhances activity detection accuracy, assesses the resilience of the algorithm to input perturbations, and investigates the effects of adopting floating-to-fixed-point conversion on algorithm performance. Simulations conducted adhere to 3GPP standards, ensuring accurate channel modeling, and employ a deep learning approach to boost the detection capabilities of mMTC GF-RA devices. The results are compelling: the algorithm achieves an exceptional 99% accuracy rate, confirming its efficacy in realworld applications.