This study addresses the challenge of accurately predicting the elastic modulus (E$_s$) of soft cohesive soils using machine learning techniques, particularly focusing on undisturbed soil sampling methods. Traditional approaches often rely on disturbed soil samples or complex in-situ testing, leading to inaccurate predictions. The research aims to develop high-performing prediction models for E$_s$ using undisturbed soil samples and Gaussian Process Regression (GPR). A new laboratory dataset is established using undisturbed cohesive soil samples obtained through a Shelby tube sampler. GPR-based prediction models are developed, with E$_s$ as the output parameter and six index properties (sand content, fine content, liquid limit, plastic limit, water content, and soil density) as input features. These features are organized into four groups for the development of four GPR-based models. The results show that a model incorporating all six input features performs exceptionally well, with R$^2$ (correlation coefficient), RMSE (root mean square error), and MAE (mean absolute error) values of 0.999, 0.054, and 0.042, respectively. The effectiveness of the optimal model is further validated using field cone penetration test (CPT) data. Sensitivity and parametric investigations reveal that soil density, water content, and Atterberg limits significantly influence the characterization of E$_s$ in cohesive soils. The study highlights the importance of undisturbed sampling methods and the potential of GPR in accurately predicting E$_s$ of soft cohesive soils.This study addresses the challenge of accurately predicting the elastic modulus (E$_s$) of soft cohesive soils using machine learning techniques, particularly focusing on undisturbed soil sampling methods. Traditional approaches often rely on disturbed soil samples or complex in-situ testing, leading to inaccurate predictions. The research aims to develop high-performing prediction models for E$_s$ using undisturbed soil samples and Gaussian Process Regression (GPR). A new laboratory dataset is established using undisturbed cohesive soil samples obtained through a Shelby tube sampler. GPR-based prediction models are developed, with E$_s$ as the output parameter and six index properties (sand content, fine content, liquid limit, plastic limit, water content, and soil density) as input features. These features are organized into four groups for the development of four GPR-based models. The results show that a model incorporating all six input features performs exceptionally well, with R$^2$ (correlation coefficient), RMSE (root mean square error), and MAE (mean absolute error) values of 0.999, 0.054, and 0.042, respectively. The effectiveness of the optimal model is further validated using field cone penetration test (CPT) data. Sensitivity and parametric investigations reveal that soil density, water content, and Atterberg limits significantly influence the characterization of E$_s$ in cohesive soils. The study highlights the importance of undisturbed sampling methods and the potential of GPR in accurately predicting E$_s$ of soft cohesive soils.