Controllable head avatar reconstruction via the inversion of few-shot images using 3D generative models has demonstrated significant potential for efficient avatar creation. However, under limited input conditions, existing one-shot inversion methods often fail to produce high-fidelity results, frequently leading to shape distortions, expression deviations, and identity inconsistencies. To address these limitations, we propose EGAvatar, a novel and efficient 3DGAN inversion framework designed to generate high-fidelity, generalizable head avatars from few-shot images. The core principle of EGAvatar is a decoupling-by-inverting strategy, built upon an animatable 3DGAN prior. Specifically, we introduce an effective animatable 3DGAN model that synthesizes high-quality 3D avatars by integrating a coarse 3D triplane representation (derived from a latent 3DGAN) with an offset 3D triplane (learned via a triplane 3DGAN). Leveraging this architecture, we design a 3DGAN-based inversion approach to reconstruct 3D avatars efficiently. Additionally, we incorporate an expression-view disentanglement mechanism to maintain consistent appearance across varying expressions and viewpoints, thereby enhancing the generalizability of avatar reconstruction from limited input images. Extensive experiments conducted on two publicly available benchmarks and a private dataset demonstrate that EGAvatar outperforms existing state-of-the-art methods in both qualitative and quantitative evaluations. Notably, EGAvatar achieves superior performance while requiring significantly fewer input images and offering more efficient training and inference.