Video generation has made significant strides with the development of diffusion models; however, achieving high temporal consistency remains a challenging task. Recently, FreeInit identified a training-inference gap and introduced a method to iteratively refine the initial noise during inference. However, iterative refinement significantly increases the computational cost associated with video generation. In this paper, we introduce FastInit, a fast noise initialization method that eliminates the need for iterative refinement. FastInit learns a Video Noise Prediction Network (VNPNet) that takes random noise and a text prompt as input, generating refined noise in a single forward pass. Therefore, FastInit greatly enhances the efficiency of video generation while achieving high temporal consistency across frames. To train the VNPNet, we create a large-scale dataset consisting of pairs of text prompts, random noise, and refined noise. Extensive experiments with various text-to-video models show that our method consistently improves the quality and temporal consistency of the generated videos. FastInit not only provides a substantial improvement in video generation but also offers a practical solution that can be applied directly during inference. The code and dataset will be released.