Traffic accidents pose a significant threat to public safety, resulting in numerous fatalities, injuries, and a substantial economic burden each year. The development of predictive models capable of real-time forecasting of post-accident impact using readily available data can play a crucial role in preventing adverse outcomes and enhancing overall safety. However, existing accident predictive models encounter two main challenges: first, reliance on either costly or non-real-time data, and second the absence of a comprehensive metric to measure post-accident impact accurately. To address these limitations, this study proposes a deep neural network model known as the cascade model. It leverages readily available real-world data from Los Angeles County to predict post-accident impacts. The model consists of two components: Long Short-Term Memory (LSTM) and Convolutional Neural Network (CNN). The LSTM model captures temporal patterns, while the CNN extracts patterns from the sparse accident dataset. Furthermore, an external traffic congestion dataset is incorporated to derive a new feature called the "accident impact" factor, which quantifies the influence of an accident on surrounding traffic flow. Extensive experiments were conducted to demonstrate the effectiveness of the proposed hybrid machine learning method in predicting the post-accident impact compared to state-of-the-art baselines. The results reveal a higher precision in predicting minimal impacts (i.e., cases with no reported accidents) and a higher recall in predicting more significant impacts (i.e., cases with reported accidents).