How would one prove the premise that a concept is not present in the training data?

With how much data is being shoveled in there, our default assumption should be that significant components are present.

That would be a weird default assumption. It's not hard to come up with new ideas. In fact, it's trivial.

And if you want to know if a specific concept is known by the LLM, you can literally ask it. It generally does a great job of telling you what it is and is not familiar with.