In Industry 4.0 manufacturing environments, forecasting Overall Equipment Efficiency (OEE) is critical for data-driven operational control and predictive maintenance. However, the highly volatile and nonlinear nature of OEE time series--particularly in complex production lines and hydraulic press systems--limits the effectiveness of forecasting. This study proposes a novel informational framework that leverages Topological Data Analysis (TDA) to transform raw OEE data into structured engineering knowledge for production management. The framework models hourly OEE data from production lines and systems using persistent homology to extract large-scale topological features that characterize intrinsic operational behaviors. These features are integrated into a SARIMAX (Seasonal Autoregressive Integrated Moving Average with Exogenous Regressors) architecture, where TDA components serve as exogenous variables to capture latent temporal structures. Experimental results demonstrate forecasting accuracy improvements of at least 17% over standard seasonal benchmarks, with Heat Kernel-based features consistently identified as the most effective predictors. The proposed framework was deployed in a Global Lighthouse Network manufacturing facility, providing a new strategic layer for production management and achieving a 7.4% improvement in total OEE. This research contributes a formal methodology for embedding topological signatures into classical stochastic models to enhance decision-making in knowledge-intensive production systems.