With the sharp increase in the number of vehicles, the issue of parking difficulties has emerged as an urgent challenge that many cities need to address promptly. In the task of predicting large-scale urban parking data, existing research often lacks effective deep learning models and strategies. To tackle this challenge, this paper proposes an innovative framework for predicting large-scale urban parking graphs leveraging real-time service capabilities, aimed at improving the accuracy and efficiency of parking predictions. Specifically, we introduce a graph attention mechanism that assesses the real-time service capabilities of parking lots to construct a dynamic parking graph that accurately reflects real preferences in parking behavior. To effectively handle large-scale parking data, this study combines graph coarsening techniques with temporal convolutional autoencoders to achieve unified dimension reduction of the complex urban parking graph structure and features. Subsequently, we use a spatio-temporal graph convolutional model to make predictions based on the coarsened graph, and a pre-trained autoencoder-decoder module restores the predicted results to their original data dimensions, completing the task. Our methodology has been rigorously tested on a real dataset from parking lots in Shenzhen. The experimental results indicate that compared to traditional parking prediction models, our framework achieves improvements of 46.8\% and 30.5\% in accuracy and efficiency, respectively. Remarkably, with the expansion of the graph's scale, our framework's advantages become even more apparent, showcasing its substantial potential for solving complex urban parking dilemmas in practical scenarios.