Well, copyright claims are usually a civil matter (in the US at least). For a civil dispute you have to make a judge or jury believe you more than the other person.

But it sounds like you are talking about a criminal charge. There the bar is higher and the government has to prove beyond a reasonable doubt. In that case I suppose the government could do things like search your computer, subpoena the AI companies for their records, talk to your editor, talk to your family and friends, etc... All the usual stuff.