Non-terrestrial networks (NTN) offer potential for efficient content broadcast in remote regions, thereby extending the reach of digital services. In this paper, we introduce a novel approach to optimize wireless edge content placement using NTN. Specifically, we dynamically select content for placement via NTN links based on popularity and suitability for delivery through NTN, while considering the orbital motion of LEO satellites. Our comprehensive system-level case studies, based on a practical LEO constellation, demonstrate the significant improvement in placement speed compared to existing methods that neglect network mobility. We further show that the advantages of NTN links over standalone wireless TN solutions are more pronounced in the early stages of content delivery and are amplified by higher content popularity correlation across geographical regions.