Wildfires are a natural phenomenon, which nowadays, due to the synergistic effect of increased human intervention and the escalation of climate change, are displaying an ever-increasing intensity and frequency. The underlying mechanisms present increased complexity, with the phenomenon itself being characterized by a significant degree of stochasticity. For the above reasons, machine learning models and neural networks are being implemented. In the current study, two types of neural networks are implemented, namely, Artificial Neural Networks (ANN) and Radial Basis Function Networks (RBF). These neural networks utilize information from the Fire Weather Index (FWI), Fosberg Fire Weather Index (FFWI), Normalized Difference Vegetation Index (NDVI) and the Normalized Difference Moisture Index (NDMI), aiming to predict ignitions in a region of Greece. All indices have been developed through the Google Earth Engine platform (GEE). In addition, a new index is proposed named “Vegetation-Enhanced FWI” (FWIveg) in order to enhance the FWI with vegetation information from the NDVI. To increase the robustness of the methodology, a genetic algorithm-based approach was used in order to obtain algorithms for the calculation of the new index. Finally, an artificial neural network was implemented in order to predict the Mati wildfire in Attica, Greece (23 July 2018) by applying the new index FWIveg, aiming to assess both the effectiveness of the new index as well as the ability to predict ignition events using neural networks. Results highlight the effectiveness of the two indices in providing joint information for fire prediction through artificial intelligence-based approaches.