Abstract: Low Earth Orbit (LEO) satellite networks, characterized by global coverage and low transmission latency, have emerged as critical infrastructures for the next generation of integrated space–ground information systems. However, the high orbital velocities of satellite nodes result in highly dynamic and time-varying network topologies. In complex space environments, these networks are particularly susceptible to various uncertainties, including node failures, link disruptions, and collisions with space debris, all of which pose significant threats to overall network robustness and service continuity. Traditional resilience evaluation methods are primarily based on static graph theory models or simplified assumptions, making it difficult to accurately characterize the structural features of dynamic, time-varying topologies. Furthermore, existing topology optimization models often suffer from insufficient coordination mechanisms among multiple objectives and neglect the global structural properties of the network, leading to difficulties in effectively balancing resilience enhancement with improvements in communication transmission performance. To address these challenges, this paper proposes a topology optimization method called GCNMO, which integrates Graph convolutional networks (GCN) with the multi-objective optimization algorithm NSGA-II. The proposed method first employs a two-layer GCN model to evaluate the resilience of satellite nodes by integrating topological and transmission features, including clustering coefficient, betweenness centrality, average hop count, and communication efficiency. This process extracts the structural significance of nodes in dynamic environments. Based on the node resilience contribution model, a weighted adjacency matrix is generated. Subsequently, a weighted natural connectivity metric is introduced as a quantitative evaluation index for resilience. This metric enhances traditional natural connectivity by incorporating node importance weights, enabling a more refined characterization of the differential contributions of various nodes to network connectivity. Building on this foundation, a heuristic nearest-neighbor linking strategy is designed that prioritizes the establishment of connections between satellite pairs that are closer in distance and exhibit higher link margins, subject to intersatellite geometric visibility and link quality constraints. This strategy generates a high-quality initial population, thereby improving the starting point for optimization. The NSGA-II algorithm is then applied to multi-objective optimization. A mathematical model is formulated with the objectives of maximizing the weighted natural connectivity and minimizing the average end-to-end delay while satisfying multiple constraints. Through the synergistic application of fast non-dominated sorting, crowding distance calculation, and an elite retention strategy, the search direction of the algorithm is guided to obtain a Pareto-optimal solution set that represents different performance tradeoffs. To validate the effectiveness of the GCNMO method, this paper demonstrates an Iridium-based simulation scenario using STK software and discusses the experiments conducted in a dynamic topology environment with 66 satellites. The results show that, compared to classic NSGA-II, the improved simulated annealing algorithm (IMOSA), and heuristic-initialization-based HNSGA2, GCNMO exhibits superior convergence speed and stability in two key metrics: weighted natural connectivity and average end-to-end delay. Under various failure scenarios, the GCNMO-optimized topologies maintain a higher global network efficiency and communication service availability. Furthermore, feature ablation experiments confirm the effectiveness of the features in the constructed node resilience contribution model, demonstrating its ability to reasonably coordinate the topological and functional robustness. This study provides a feasible approach that integrates graph neural networks and multi-objective evolutionary algorithms to optimize the resilience of dynamic satellite networks, offering both theoretical value and engineering reference significance.