Increased drone proliferation in civilian and professional settings has created new threat vectors for airports and national infrastructures. The economic damage for a single major airport from drone incursions is estimated to be millions per day. Due to the lack of diverse drone training data, accurate training of deep learning detection algorithms under scarce data is an open challenge. Existing methods largely rely on collecting diverse and comprehensive experimental drone footage data, artificially induced data augmentation, transfer and meta-learning, as well as physics-informed learning. However, these methods cannot guarantee capturing diverse drone designs and fully understanding the deep feature space of drones. Here, we show how understanding the general distribution of the drone data via a Generative Adversarial Network (GAN) and explaining the missing features using Topological Data Analysis (TDA) - can allow us to acquire missing data to achieve rapid and more accurate learning. We demonstrate our results on a drone image dataset, which contains both real drone images as well as simulated images from computer-aided design. When compared to random data collection (usual practice - discriminator accuracy of 94.67\% after 200 epochs), our proposed GAN-TDA informed data collection method offers a significant 4\% improvement (99.42\% after 200 epochs). We believe that this approach of exploiting general data distribution knowledge form neural networks can be applied to a wide range of scarce data open challenges.