The increasing concerns regarding data privacy have triggered a paradigm shift in machine learning (ML) systems, moving the inference and part of the training process from the cloud, which continues to perform model updates, to the deep edge. This new approach, known as Federated Learning (FL), reduces the workloads on the remote servers and network infrastructure, while enhancing overall data privacy. Recent research has shown that inference for Artificial Neural Networks (ANNs) can be efficiently executed on microcontroller units (MCUs). However, the training phase still heavily relies on cloud computing and requires the transfer of large amounts of data over the network. This paper explores the feasibility of training an ML model from scratch at the deep edge using two distinct datasets, CogDist and the Car Evaluation Dataset. The proposed approach introduces a decentralized training solution optimized for resource-constrained devices by leveraging a lightweight variant of stochastic gradient descent (SGD) called L-SGD. L-SGD is tailored for maximum speed and minimal memory usage on the Arm Cortex-M MCU family, including Arm Cortex-M7, Arm Cortex-M4, and Arm Cortex-M0+. For fully-connected ANNs trained on the selected datasets, empirical results show that L-SGD can reduce both the overall execution time and the memory footprint, when compared to the original SGD approach, while keeping the same performance in terms of Precision, Recall, F1-score, and Accuracy.