Product retrieval is the backbone of e-commerce search: for each user query, it identifies a high-recall candidate set from billions of items, laying the foundation for high-quality ranking and user experience. Despite extensive optimization for mainstream queries, existing systems still struggle with long-tail queries, especially knowledge-intensive ones. These queries exhibit diverse linguistic patterns, often lack explicit purchase intent, and require domain-specific knowledge reasoning for accurate interpretation. They also suffer from a shortage of reliable behavioral logs, which makes such queries a persistent challenge for retrieval optimization. To address these issues, we propose an efficient data synthesis framework tailored to retrieval involving long-tail, knowledge-intensive queries. The key idea is to implicitly distill the capabilities of a powerful offline query-rewriting model into an efficient online retrieval system. Leveraging the strong language understanding of LLMs, we train a multi-candidate query rewriting model with multiple reward signals and capture its rewriting capability in well-curated query-product pairs through a powerful offline retrieval pipeline. This design mitigates distributional shift in rewritten queries, which might otherwise limit incremental recall or introduce irrelevant products. Experiments demonstrate that without any additional tricks, simply incorporating this synthetic data into retrieval model training leads to significant improvements. Online Side-By-Side (SBS) human evaluation results indicate a notable enhancement in user search experience.