This study aims to accurately estimate vertical tire forces on racing tires of specific stiffness using acceleration, pressure, and speed data measurements from a test rig. A hybrid model, termed Random Forest Assisted Deep Neural Network (RFADNN), is introduced, combining a novel deep learning framework with the Random Forest Algorithm to enhance estimation accuracy. By leveraging the Temporal Convolutional Network (TCN), Minimal Gated Unit (MGU), Long Short-Term Memory (LSTM), and Attention mechanisms, the deep learning framework excels in extracting complex features, which the Random Forest Model subsequently analyzes to improve the accuracy of estimating vertical tire forces. Validated with test data, this approach outperforms standard models, achieving an MAE of 0.773 kgf, demonstrating the advantage of the RFADNN method in required vertical force estimation tasks for race tires. This comparison emphasizes the significant benefits of incorporating advanced deep learning with traditional machine learning to provide a comprehensive and interpretable solution for complex estimation challenges in automotive engineering.