The ubiquitous deployment of deep learning systems on resource-constrained Edge devices is hindered by their high computational complexity coupled with their fragility to out-of-distribution (OOD) data, especially to naturally occurring common corruptions. Current solutions rely on the Cloud to train and compress models before deploying to the Edge. This incurs high energy and latency costs in transmitting locally acquired field data to the Cloud while also raising privacy concerns. We propose GEARnn (Growing Efficient, Accurate, and Robust neural networks) to grow and train robust networks in-situ, i.e., completely on the Edge device. Starting with a low-complexity initial backbone network, GEARnn employs One-Shot Growth (OSG) to grow a network satisfying the memory constraints of the Edge device using clean data, and robustifies the network using Efficient Robust Augmentation (ERA) to obtain the final network. We demonstrate results on a NVIDIA Jetson Xavier NX, and analyze the trade-offs between accuracy, robustness, model size, energy consumption, and training time. Our results demonstrate the construction of efficient, accurate, and robust networks entirely on an Edge device.