In this paper, we present a novel method to significantly enhance the computational efficiency of Adaptive Spatial-Temporal Graph Neural Networks (ASTGNNs) by introducing the concept of the Graph Winning Ticket (GWT), derived from the Lottery Ticket Hypothesis (LTH). By adopting a pre-determined star topology as a GWT prior to training, we balance edge reduction with efficient information propagation, reducing computational demands while maintaining high model performance. Both the time and memory computational complexity of generating adaptive spatial-temporal graphs is significantly reduced from O(N²) to O(N). Our approach streamlines the ASTGNN deployment by eliminating the need for exhaustive training, pruning, and retraining cycles, and demonstrates empirically across various datasets that it is possible to achieve comparable performance to full models with substantially lower computational costs. Specifically, our approach enables training ASTGNNs on the largest scale spatial-temporal dataset using a single A6000 equipped with 48 GB of memory, overcoming the out-of-memory issue encountered during original training and even achieving state-of-the-art performance. Furthermore, we delve into the effectiveness of the GWT from the perspective of spectral graph theory, providing substantial theoretical support. This advancement not only proves the existence of efficient sub-networks within ASTGNNs but also broadens the applicability of the LTH in resource-constrained settings, marking a significant step forward in the field of graph neural networks. Code is available at https://anonymous.4open.science/r/paper-1430.