That's the neat thing, you don't.
LLM training is primarily about getting the LLM to understand concepts. When you need it to be factual, or are working with it to solve novel problems, you can put a bunch of relevant information into the LLM's context and it can use that even if it wasn't explicitly trained on it. It's called RAG, retrieval-augmented generation. Most of the general-purpose LLMs on the net these days do that, when you ask Copilot or Gemini about stuff it'll often have footnotes in the response that point to the stuff that it searched up in the background and used as context.
So for a future Stack Overflow LLM replacement, I'd expect the LLM to be backed up by being able to search through relevant documentation and source code.
How does this play out when you hold a human contributor to the same standards? They also often fail to summarize information accurately or bring up the wrong thing. Lots of answers on Stack Overflow are just plain wrong, or focus on the wrong thing, or don't reference the correct sources (when they reference anything at all). The most common criticism of Stack Overflow I'm seeing is how its human contributors direct people to other threads and declare that the question is "already answered" there when it isn't really.
LLMs can do a decent job. And right now they are as bad as they're ever going to be.