Recent advances in deep learning-based medical image registration have shown that training deep neural networks~(DNNs) does not necessarily require medical images. Previous work showed that DNNs trained on randomly generated images with carefully designed noise and contrast properties can still generalize well to unseen medical data. Building on this insight, we propose using registration between random images as a proxy task for pretraining a foundation model for image registration. Empirical results show that our pretraining strategy improves registration accuracy, reduces the amount of domain-specific data needed to achieve competitive performance, and accelerates convergence during downstream training, thereby enhancing computational efficiency.