The latest two-stage optimization framework based on graph neural network (GNN) and large neighborhood search (LNS) is the most popular framework in solving large-scale integer programs (IPs). However, the framework can not effectively use the embedding spatial information in GNN and still highly relies on large-scale solvers in LNS, resulting in the scale of IP being limited by the ability of the current solver and performance bottlenecks. To handle these issues, this paper presents a GNN&GBDT-guided fast optimizing framework for large-scale IPs that only uses a small-scale optimizer to solve large-scale IPs efficiently. Specifically, the proposed framework can be divided into three stages: Multi-task GNN Embedding to generate the embedding space, GBDT Prediction to effectively use the embedding spatial information, and Neighborhood Optimization to solve large-scale problems fast using the small-scale optimizer. Extensive experiments show that the proposed framework can solve IPs with millions of scales and surpass SCIP and Gurobi in the specified wall-clock time using only a small-scale optimizer with 30% of the problem size. It also shows that the proposed framework can save 99% of running time in achieving the same solution quality as SCIP, which verifies the effectiveness and efficiency of the proposed framework in solving large-scale IPs.