Deep learning recommendation systems at scale have provided remarkable gains through increasing model capacity (i.e. wider and deeper neural networks), but it comes at significant training cost and infrastructure cost. Model pruning is an effective technique to reduce computation overhead for deep neural networks by removing redundant parameters. However, modern recommendation systems are still thirsty for model capacity due to the demand for handling big data. Thus, pruning a recommendation model at scale results in a smaller model capacity and consequently lower accuracy. To reduce computation cost without sacrificing model capacity, we propose a dynamic training scheme, namely alternate model growth and pruning, to alternatively construct and prune weights in the course of training. Our method leverages structured sparsification to reduce computational cost without hurting the model capacity at the end of offline training so that a full-size model is available in the recurring training stage to learn new data in real-time. To the best of our knowledge, this is the first work to provide in-depth experiments and discussion of applying structural dynamics to recommendation systems at scale to reduce training cost. The proposed method is validated with an open-source deep-learning recommendation model (DLRM) and state-of-the-art industrial-scale production models.