Dialogue State Tracking (DST) is crucial for linking user intentions to appropriate services in task-oriented dialogue systems. We propose a zero-shot, scheme-only approach that tackles two main challenges: generating synthetic dialogues that balance diversity with schema alignment, and efficiently distilling knowledge from a large language model (LLM) into a smaller model. Our pipeline first creates scenarios, dialogue logic flows, and utterances via dynamic complexity prompting, eliminating reliance on handcrafted templates. We then use a two-stage distillation process to learn formalized dialogue representations and DST related chain-of-thought reasoning. This structure preserves interpretive capabilities while reducing inference overhead. Experiments on the MultiWOZ benchmark show that our method achieves state-of-the-art performance under zero-shot, scheme-only situation and generalizes effectively to few-shot scenarios, offering a practical and scalable solution for domains lacking real data.