Originally, space situational awareness focused on space objects’ detection, tracking and identification using ground-based systems. However, with the rapid deployment of low Earth orbit (LEO) mega constellations and the continuous increase of space debris, such large-scale space objects pose significant challenges to traditional ground-based observation mode. Comparatively, the space-based situational awareness constellation has not only the advantages of maneuverability and all-weather operation, but also the observation mode of space-based observation and multi satellite cooperation, which can effectively improve the coverage efficiency and observation accuracy of large-scale space objects. Full coverage of space objects is the foundation and key for constellations to achieve space-based situational awareness. Addressing the issue of full coverage of large-scale space objects, a reasonable constellation configuration design method can shorten the time required to traverse all objects while satisfying coverage constraints. Therefore, a constellation configuration optimization solution method for rapid coverage observation of large-scale space objects is proposed. Firstly, the space operational scenario of the large-scale space objects is modeled and simulated. Then, performance indicators such as coverage rate, completion time of full coverage and average coverage duration are modeled and converted into numerical indicators, and are set as multiple optimization objectives of Non-Dominated Sorting Genetic Algorithm III (NSGA-III) algorithm. Finally, the NSGA-III algorithm is used to solve the optimal constellation configuration parameters for observing large-scale space objects. The simulation results show that the method is correct and easy to implement, and can achieve full coverage of large-scale space objects with over 10000 satellites or debris within 4 h.