Technological advancements in Machine learning, artificial intelligence (AI), and data science are bringing industries to the era of the fourth industrial revolution. The application of machine learning in chemical engineering is in the domains of process modeling, optimization, and predictive analysis. Traditional process modeling relies heavily on first-principal methods, which, while accurate, are computationally demanding and are non-flexible for variable process conditions. Green methanol produced through the power-to-liquid (PtL) process has gained significant popularity due to its various applications in household items, as a raw material for manufacturing valuable chemicals, and as a fuel both in blend or pure form. In today's competitive and uncertain chemical industry market, fast and accurate models are required to predict the plant output. This work aims to develop a surrogate model of the methanol production process based on the data-driven technique and using machine learning to predict energy requirements, final product purity, and methanol production rate. The effect of the sampling size and sampling technique (mainly Latin-Hypercube Sampling - LHS, Monte Carlo, and SOBOL) on the performance of the surrogate model is evaluated. A comparative analysis of different machine learning (e.g., XG-Boost, Random Forest, Decision Tree, Support Vector Regression) and Deep learning models (e.g., Artificial Neural Networks) is conducted using metrics such as coefficient of determination (R²), mean-squared error (MSE), and mean-absolute-error (MAE). Additionally, this work explores the use of these trained machine learning models in optimizing process conditions to maximize production rate, enhance product purity, and reduce energy requirements.