Generative query suggestion, powered by Large Language Models (LLMs), has become increasingly popular in search and conversational systems to reduce user friction and guide intent formulation. Existing approaches align suggestions with user preferences (e.g., clicks or conversions). This works for open-ended applications like chatbots and personal assistants, where the result space is unconstrained or historical user free-text queries are abundant. However, applying these methods to travel search presents two limitations. First, travel search is fundamentally constrained by physical inventory; a query (e.g., "romantic beachfront villa") may yield abundant results in Bali but few in Tokyo, so aligning with user preferences is not by itself grounded in what can be offered. Second, travel platforms traditionally rely on faceted search interfaces with no free-text queries. This creates a cold-start problem: without historical query logs there is no demand-side data for alignment, and without a seed query at request time, suggestions must be generated proactively from structured context alone. To address these challenges, we propose SCOUT, a bootstrapping framework for supply-aware proactive query suggestion. SCOUT overcomes the data gap by substituting missing demand-side user feedback with supply-side system feedback. It treats the search engine as a reinforcement learning environment, deriving a dense reward from the production reranker's query-listing match scores, and optimizes the policy with Group Relative Policy Optimization (GRPO). SCOUT improves inventory match rate (IMR@18) by 12.3% while preserving diversity, matching a compute-intensive best-of-8 policy at zero marginal inference cost and making supply-aware suggestion deployable on a real-time travel search path.

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