We present FastAvatar, a fast and robust algorithm for single-image 3D face reconstruction using 3D Gaussian Splatting (3DGS). Given a single input image from an arbitrary pose, FastAvatar recovers a high-quality, full-head 3DGS avatar in approximately 3 seconds on a single NVIDIA A100 GPU. We use a two-stage design: a feed-forward encoder-decoder predicts coarse face geometry by regressing Gaussian structure from a pose-invariant identity embedding, and a lightweight test-time refinement stage then optimizes the appearance parameters for photorealistic rendering. This hybrid strategy combines the speed and stability of direct prediction with the accuracy of optimization, enabling strong identity preservation even under extreme input poses. FastAvatar achieves state-of-the-art reconstruction quality (24.01 dB PSNR, 0.91 SSIM) while running over 600x faster than existing per-subject optimization methods (e.g., FlashAvatar, GaussianAvatars, GASP). Once reconstructed, our avatars support photorealistic novel-view synthesis and FLAME-guided expression animation, enabling controllable reenactment from a single image. By jointly offering high fidelity, robustness to pose, and rapid reconstruction, FastAvatar significantly broadens the applicability of 3DGS-based facial avatars.