Climate change mitigation necessitates increased investment in green sectors. This study proposes a methodology to predict green finance growth across various countries, aiming to encourage such investments. Our approach leverages time-series Conditional Generative Adversarial Networks (CT-GANs) for data augmentation and Nonlinear Autoregressive Neural Networks (NARNNs) for prediction. The green finance growth predicting model was applied to datasets collected from forty countries across five continents. The Augmented Dickey-Fuller (ADF) test confirmed the non-stationary nature of the data, supporting the use of Nonlinear Autoregressive Neural Networks (NARNNs). CT-GANs were then employed to augment the data for improved prediction accuracy. Results demonstrate the effectiveness of the proposed model. NARNNs trained with CT-GAN augmented data achieved superior performance across all regions, with R-squared (R2) values of 98.8%, 96.6%, and 99% for Europe, Asia, and other countries respectively. While the RMSE for Europe, Asia, and other countries are 1.26e+2, 2.16e+2, and 1.16e+2 respectively. Compared to a baseline NARNN model without augmentation, CT-GAN augmentation significantly improved both R2 and RMSE. The R2 values for the Europe, Asia, and other countries models are 96%, 73%, and 97.2%, respectively. The RMSE values for the Europe, Asia, and various countries models are 2.24e+2, 7e+2, and 2.07e+2, respectively. The Nonlinear Autoregressive Exogenous Neural Network (NARX-NN) exhibited significantly lower performance across Europe, Asia, and other countries with R2 values of 74%, 52%, and 86%, and RMSE values of 1.11e+2, 3.63e+2, and 1.8e+2, respectively.