Sun is the sustainable and abundantly available alternative resource on the planet Earth. The uncertain nature of the source caused due to various environmental factors increases the need to quantify the irradiation potential at the targeted location, especially for power smoothing processes, solar-fed electrical applications, and the utility grid. The irradiation measuring devices lead to appropriate maintenance and more expenses and are ineffective under dynamically varying irradiation conditions. Hence, a robust ML-based forecasting technique is sufficient to predict GHI under dynamically varying irradiation profiles caused by various environmental factors. Therefore, this study focuses on short-term (hourly) GHI forecasting using the FFBP-LM-ANN approach. In most of the related articles, the selection of independent variables and designing the network is being a challenge and obstacle in attaining fast and efficient prediction. Such a scenario increases the overall computation complexity and understanding. Hence, this study was intended to use a simple process to crucially select 5 environmental factors and to optimally choose the number of neurons for designing the network for better irradiation prediction. Thus, the network is designed with an input layer of 5 selected environmental variables and one hidden layer with 20 neurons, and hourly GHI in the output layer is performed. The approach is trained using the Levenberg-Marquardt BP algorithm in MATLAB toolbox, with the help of a 4-year dataset received for the rooftop panels of VIT University, Chennai, from NREL. The performance of the model during training and testing was validated and analyzed using 9 performance matrices. As a result, FFBP-LM-ANN satisfactorily predicts hourly GHI for the targeted location based on rRMSE of 7.21%, MAE of 0.042, MBE of 0.000492, R of 0.96, MAPE of 44.4%, MRE of 9.5%, and NSE of 94% obtained under testing process. Moreover, the model has performed much better when compared with 9 related models that exist in literature based on the input variables used, network design, epoch, and RMSE. Subsequently, such a predictor will be adaptable and more suitable for the explicit prediction of hourly GHI for different regions across the world having varying climatic conditions, since the study model is designed for locations facing robust climatic nature. More importantly, the designed model is superior with only environmental variables, which are rarely found in the article, rather than geographical variables, which are predominantly used in most of the related literature.