Yes, they do. In a court. To Judge Dearie, the appointed Special Master. What Trump says in a tweet, a "truth" or a Hannity interview is legally meaningless. Trump, via his lawyers, must say he ordered the documents declassified. If he doesn't, Judge Dearie will likely rule that they remain classified at the level assigned by the classifying authority.
To be clear, the Special Master has no authority to declassify the documents. He can only determine if TRUMP declassified them on or before 20 Jan 2021 or not. To do that, Trump's lawyers must provide some document or testimony that he did, in fact declassify them.