If you mean ads served as part of the response, and not explicitly marked as ads, then there is nothing you can do. They are like sponsored sections and product placement in YT videos, and no ad blocker can help you. That being said, you have no guarantee that this won't happen even if you pay for an LLM. In fact people paying for Youtube are still subject to in-video advertising.

Self-hosting open source models will be the best thing to do as models and inference engines become more optimized, and hardware becomes faster.