Rainfall prediction, a type of weather forecasting, has a big impact on agriculture and farming, as well as other industries like natural disaster management. One of the most crucial aspects of today's climate is accurate and timely rainfall prediction. Such issues could be avoided if worst-case weather scenarios could be predicted ahead of time and timely warnings issued. The "nonlinear autoregressive (AR) with exogenous inputs" (NARX) neural network (NN) prediction model has been introduced in this paper for the prediction of rainfall using historical geographical data from the Kashmir province of the union territory of Jammu & Kashmir, India. The methodology was developed using six years of historical-geographical data from three different substations in Kashmir. Four explanatory independent variables like maximum temperature, minimum temperature, humidity measured at 12 a.m., and humidity measured at 3 p.m. as well as a target variable indicating the amount of rainfall were considered. For a better computational time and performance accuracy, the proposed algorithm is trained using the grey wolf optimizer (GWO) and the Levenberg-Marquardt (LM) algorithms. The grey wolf Levenberg-Marquardt (GWLM) and NARX implementation methodology was deemed one of the best-fit models. The obtained values for the mean squared error (MSE) and regression value (R) predictions are 3.12% and 0.9899% in the case of training. The values are 0.144% and 0.9936% in validation, and 0.311% and 0.9988% in testing. The suggested model was then compared to a number of traditional and ensemble machine learning (ML) methods, and it was determined that the proposed model performs better with less processing time. The grey wolf Levenberg-Marquardt nonlinear AR with external inputs (GWLM-NARX) model is found to be a more practical neural network model to use.