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Large-scale low Earth orbit satellite networks (LSNs) have been attracting increasing attention in recent years. These systems offer advantages such as low latency, high bandwidth communication, and all terrain coverage. However, the main challenges faced by LSNs is the calculation and maintenance of routing strategies. This is primarily due to the large scale and dynamic network topology of LSN constellations. As the number of satellites in constellations continues to rise, the feasibility of the centralized routing strategy, which calculates all shortest routes between every satellite, becomes increasingly limited by space and time constraints. This approach is also not suitable for the Walker Delta formation, which is becoming more popular for giant constellations. In order to find an effective routing strategy, this paper defines the satellite routing problem as a mixed linear integer programming problem (MILP), proposes a routing strategy based on a genetic algorithm (GA), and comprehensively considers the efficiency of source or destination ground stations to access satellite constellations. The routing strategy integrates ground station ingress and exit policies and inter-satellite packet forwarding policies and reduces the cost of routing decisions. The experimental results show that, compared with the traditional satellite routing algorithm, the proposed routing strategy has better link capacity utilization, a lower round trip communication time, and an improved traffic reception rate.