Zero-shot domain adaptation is a method for adapting a model to a target domain without utilizing target domain image data. To enable adaptation without target images, existing studies utilize CLIP's embedding space and text description to simulate target-like style features. Despite the previous achievements in zero-shot domain adaptation, we observe that these text-driven methods struggle to capture complex real-world variations and significantly increase adaptation time due to their alignment process. Instead of relying on text descriptions, we explore solutions leveraging image data, which provides diverse and more fine-grained style cues. In this work, we propose SIDA, a novel and efficient zero-shot domain adaptation method leveraging synthetic images. To generate synthetic images, we first create detailed, source-like images and apply image translation to reflect the style of the target domain. We then utilize the style features of these synthetic images as a proxy for the target domain. Based on these features, we introduce Domain Mix and Patch Style Transfer modules, which enable effective modeling of real-world variations. In particular, Domain Mix blends multiple styles to expand the intra-domain representations, and Patch Style Transfer assigns different styles to individual patches. We demonstrate the effectiveness of our method by showing state-of-the-art performance in diverse zero-shot adaptation scenarios, particularly in challenging domains. Moreover, our approach achieves high efficiency by significantly reducing the overall adaptation time.