Despite significant progress in 3D avatar reconstruction, it still faces challenges such as high time complexity, sensitivity to data quality, and low data utilization. We propose FastAvatar, a feedforward 3D avatar framework capable of flexibly leveraging diverse daily recordings (e.g., a single image, multi-view observations, or monocular video) to reconstruct a high-quality 3D Gaussian Splatting (3DGS) model within seconds, using only a single unified model. The core of FastAvatar is a Large Gaussian Reconstruction Transformer (LGRT) featuring three key designs: First, a 3DGS transformer aggregating multi-frame cues while injecting initial 3D prompt to predict the corresponding registered canonical 3DGS representations; Second, multi-granular guidance encoding (camera pose, expression coefficient, head pose) mitigating animation-induced misalignment for variable-length inputs; Third, incremental Gaussian aggregation via landmark tracking and sliced fusion losses. Integrating these features, FastAvatar enables incremental reconstruction, i.e., improving quality with more observations without wasting input data as in previous works. This yields a quality-speed-tunable paradigm for highly usable 3D avatar modeling. Extensive experiments show that FastAvatar has a higher quality and highly competitive speed compared to existing methods.