Identifying algorithms for computational efficient unsupervised training of large language models is an important and active area of research. In this work, we develop and study a straightforward, dynamic always-sparse pre-training approach for BERT language modeling task, which leverages periodic compression steps based on magnitude pruning followed by random parameter re-allocation. This approach enables us to achieve Pareto improvements in terms of the number of floating-point operations (FLOPs) over statically sparse and dense models across a broad spectrum of network sizes. Furthermore, we demonstrate that training remains FLOP-efficient when using coarse-grained block sparsity, making it particularly promising for efficient execution on modern hardware accelerators.