Recommending cold items remains a significant challenge in billion-scale online recommendation systems. While warm items benefit from historical user behaviors, cold items rely solely on content features, limiting their recommendation performance and impacting user experience and revenue. Current models generate synthetic behavioral embeddings from content features but fail to address the core issue: the absence of historical behavior data. To tackle this, we introduce the LLM Simulator framework, which leverages large language models to simulate user interactions for cold items, fundamentally addressing the cold-start problem. However, simply using LLM to traverse all users can introduce significant complexity in billion-scale systems. To manage the computational complexity, we propose a coupled funnel ColdLLM framework for online recommendation. ColdLLM efficiently reduces the number of candidate users from billions to hundreds using a trained coupled filter, allowing the LLM to operate efficiently and effectively on the filtered set. Extensive experiments show that ColdLLM significantly surpasses baselines in cold-start recommendations, including Recall and NDCG metrics. A two-week A/B test also validates that ColdLLM can effectively increase the cold-start period GMV.