The large and catastrophic wildfires have been increasing across the globe in the recent decade, highlighting the importance of simulating and forecasting fire dynamics in near real-time. This is extremely challenging due to the complexities of physical models and geographical features. Running physics-based simulations for large wildfire events in near real-time are computationally expensive, if not infeasible. In this work, we develop and test a novel data-model integration scheme for fire progression forecasting, that combines Reduced-order modelling, recurrent neural networks (Long-Short-Term Memory), data assimilation, and error covariance tuning. The Reduced-order modelling and the machine learning surrogate model ensure the efficiency of the proposed approach while the data assimilation enables the system to adjust the simulation with observations. We applied this algorithm to simulate and forecast three recent large wildfire events in California from 2017 to 2020. The deep-learning-based surrogate model runs around 1000 times faster than the Cellular Automata simulation which is used to generate training data-sets. The daily fire perimeters derived from satellite observation are used as observation data in Latent Assimilation to adjust the fire forecasting in near real-time. An error covariance tuning algorithm is also performed in the reduced space to estimate prior simulation and observation errors. The evolution of the averaged relative root mean square error (R-RMSE) shows that data assimilation and covariance tuning reduce the RMSE by about 50% and considerably improves the forecasting accuracy. As a first attempt at a reduced order wildfire spread forecasting, our exploratory work showed the potential of data-driven machine learning models to speed up fire forecasting for various applications.