Abstract: With the latest advances in deep learning, several methods have been investigated for optimal learning settings in scenarios where the data stream is continuous over time. However, sparse networks training in such settings have often been overlooked. In this paper, we explore the problem of training a neural network with a target sparsity in a particular case of online learning: the anytime learning at macroscale paradigm (ALMA). We propose a novel way of progressive pruning, referred to as \textit{Anytime Progressive Pruning} (APP); the proposed approach significantly outperforms the baseline dense and Anytime OSP models across multiple architectures and datasets under short, moderate, and long-sequence training. Our method, for example, shows an improvement in accuracy of $\approx 7\%$ and a reduction in the generalisation gap by $\approx 22\%$, while being $\approx 1/3$ rd the size of the dense baseline model in few-shot restricted imagenet training. The code and experiment dashboards can be accessed at \url{https://github.com/landskape-ai/Progressive-Pruning} and \url{https://wandb.ai/landskape/APP}, respectively.