That's not how defamation laws work. The NYTimes is liable for publishing the document, and it's not up to Trump to disprove them, but up to the NYTimes to prove that the document they have is not a fake.
Given that their source is wholly anonymous, I'm skeptical. There's nothing that indicates any credible path from Trump to the source.
That's also not how defamation laws work. Trump is obviously a public figure, so to succeed in a defamation suit against the New York Times, the burden would be on him to prove that the NYT acted with
actual malice in publishing a fraudulent document. It wouldn't even be enough for Trump to prove that the document was fraudulent. He'd have to show that either the NYT
knew it was fraudulent or that the NYT acted with reckless disregard as to whether or not it was legitimate. He'd lose. Badly.