Low earth orbit (LEO) satellite-assisted communications have been considered as one of the key elements in beyond 5G systems to provide wide coverage and cost-efficient data services. Such dynamic space-terrestrial topologies impose an exponential increase in the degrees of freedom in network management. In this paper, we address two practical issues for an over-loaded LEO-terrestrial system. The first challenge is how to efficiently schedule resources to serve a massive number of connected users, such that more data and users can be delivered/served. The second challenge is how to make the algorithmic solution more resilient in adapting to dynamic wireless environments. We first propose an iterative suboptimal algorithm to provide an offline benchmark. To adapt to unforeseen variations, we propose an enhanced meta-critic learning algorithm (EMCL), where a hybrid neural network for parameterization and the Wolpertinger policy for action mapping are designed in EMCL. The results demonstrate EMCL’s effectiveness and fast-response capabilities in over-loaded systems and in adapting to dynamic environments compare to previous actor-critic and meta-learning methods.