The emerging SAT communication network holds great promise in various wireless access applications and services. How to achieve in such integrated network the best data delivery performance across multiple layers, given the limited inter-layer link capacity, however, is still a challenging issue. To the best of our knowledge, the cross-layer gateway selection problem for traffic transmission remains almost untouched, since previous works in this line mainly focused on one single layer and neglected the other layers. Toward this end, we first define in this article the cross-layer gateway selection as a constrained optimization problem in a SAT network, and then propose a greedy solution to efficiently identify an optimal set of gateways from an aerial network that serves as a relay layer for the data delivery between the terrestrial layer and the satellite layer. After providing extensive numerical results to validate the efficacy of our solution, we also point out challenges and future directions.