This study presents a novel approach for accurate State of Health (SOH) estimation in lithium-ion batteries (LIBs) using an optimized Feed-Forward Neural Network (FNN) model without back-propagation. The proposed method leverages key health features (HFs) extracted from discharge voltage data, including the area under the voltage curve and selected polynomial regression coefficients. By systematically optimizing the hidden-layer architecture based on minimal Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), the model effectively mitigates overfitting and enhances generalization. Experimental validation on the Oxford Battery dataset demonstrates that the proposed FNN model achieves superior accuracy. The results show a significant improvement in SOH estimation, with a RMSE of less than 0.14%, outperforming other refrences. This methodology provides a scalable solution for real-time battery health monitoring, ensuring reliable performance for second-life applications.