One of the most important functions of the battery management system (BMS) in battery electric vehicle (BEV) applications is to estimate the state of charge (SOC). In this study, several machine and deep learning techniques, such as linear regression, support vector regressors (SVRs), k-nearest neighbor, random forest, extra trees regressor, extreme gradient boosting, random forest combined with gradient boosting, artificial neural networks (ANNs), convolutional neural networks, and long short-term memory (LSTM) networks, are investigated to develop a modeling framework for SOC estimation. The purpose of this study is to improve overall battery performance by examining how BEV operation affects battery deterioration. By using dynamic response simulation of lithium battery electric vehicles (BEVs) and lithium battery packs (LIBs), the proposed research provides realistic training data, enabling more accurate prediction of SOC using data-driven methods, which will have a crucial and effective impact on the safe operation of electric vehicles. The paper evaluates the performance of machine and deep learning algorithms using various metrics, including the R2 Score, median absolute error, mean square error, mean absolute error, and max error. All the simulation tests were performed using MATLAB 2023, Anaconda platform, and COMSOL Multiphysics.