This paper aims to introduce 3D Gaussian for efficient, expressive, and editable digital avatar generation. This task faces two major challenges: (1) The unstructured nature of 3D Gaussian makes it incompatible with current generation pipelines; (2) the expressive animation of 3D Gaussian in a generative setting that involves training with multiple subjects remains unexplored. In this paper, we propose a novel avatar generation method named $E^3$Gen, to effectively address these challenges. First, we propose a novel generative UV features plane representation that encodes unstructured 3D Gaussian onto a structured 2D UV space defined by the SMPL-X parametric model. This novel representation not only preserves the representation ability of the original 3D Gaussian but also introduces a shared structure among subjects to enable generative learning of the diffusion model. To tackle the second challenge, we propose a part-aware deformation module to achieve robust and accurate full-body expressive pose control. Extensive experiments demonstrate that our method achieves superior performance in avatar generation and enables expressive full-body pose control and editing.