Grain Growth strongly influences the mechanical behavior of materials, making its prediction a key objective in microstructural engineering. In this study, several deep learning approaches were evaluated, including recurrent neural networks (RNN), long short-term memory (LSTM), temporal convolutional networks (TCN), and transformers, to forecast grain size distributions during grain growth. Unlike full-field simulations, which are computationally demanding, the present work relies on mean-field statistical descriptors extracted from high-fidelity simulations. A dataset of 120 grain growth sequences was processed into normalized grain size distributions as a function of time. The models were trained to predict future distributions from a short temporal history using a recursive forecasting strategy. Among the tested models, the LSTM network achieved the highest accuracy (above 90\%) and the most stable performance, maintaining physically consistent predictions over extended horizons while reducing computation time from about 20 minutes per sequence to only a few seconds, whereas the other architectures tended to diverge when forecasting further in time. These results highlight the potential of low-dimensional descriptors and LSTM-based forecasting for efficient and accurate microstructure prediction, with direct implications for digital twin development and process optimization.