Pre-search query recommendation, widely known as HintQ on Taobao's homepage, plays a vital role in intent capture and demand discovery, yet traditional methods suffer from shallow semantics, poor cold-start performance and low serendipity due to reliance on ID-based matching and co-click heuristics. To overcome these challenges, we propose AIGQ (AI-Generated Query architecture), the first end-to-end generative framework for HintQ scenario. AIGQ is built upon three core innovations spanning training paradigm, policy optimization and deployment architecture. First, we propose Interest-Aware List Supervised Fine-Tuning (IL-SFT), a list-level supervised learning approach that constructs training samples through session-aware behavior aggregation and interest-guided re-ranking strategy to faithfully model nuanced user intent. Accordingly, we design Interest-aware List Group Relative Policy Optimization (IL-GRPO), a novel policy gradient algorithm with a dual-component reward mechanism that jointly optimizes individual query relevance and global list properties, enhanced by a model-based reward from the online click-through rate (CTR) ranking model. To deploy under strict real-time and low-latency requirements, we further develop a hybrid offline-online architecture comprising AIGQ-Direct for nearline personalized user-to-query generation and AIGQ-Think, a reasoning-enhanced variant that produces trigger-to-query mappings to enrich interest diversity. Extensive offline evaluations and large-scale online A/B experiments on Taobao demonstrate that AIGQ consistently delivers substantial improvements in key business metrics across platform effectiveness and user engagement.