Contemporary automatic first break (FB) picking methods typically analyze 1D signals, 2D source gathers, or 3D source-receiver gathers. Utilizing higher-dimensional data, such as 2D or 3D, incorporates global features, improving the stability of local picking. Despite the benefits, high-dimensional data requires structured input and increases computational demands. Addressing this, we propose a novel approach using deep graph learning called DGL-FB, constructing a large graph to efficiently extract information. In this graph, each seismic trace is represented as a node, connected by edges that reflect similarities. To manage the size of the graph, we develop a subgraph sampling technique to streamline model training and inference. Our proposed framework, DGL-FB, leverages deep graph learning for FB picking. It encodes subgraphs into global features using a deep graph encoder. Subsequently, the encoded global features are combined with local node signals and fed into a ResUNet-based 1D segmentation network for FB detection. Field survey evaluations of DGL-FB show superior accuracy and stability compared to a 2D U-Net-based benchmark method.