I don't know what authentication information is stored in an email header that would be difficult to fake. But if the email is stored on a third party's server, the chain of custody and time of creation can be independently documented.
For an old email, it would be up to the opposing counsel to argue that the person who made it made it for the purpose of fabricating evidence however many years ago.
Plenty of evidence accepted in court can be faked. A written ransom note might be faked. A receipt for a gun could be faked.
How believable the emails are will vary. Do you still have the headers? Is there a valid DKIM signature in those headers? Can you bring the people CCed on the email as witnesses? etc.
For an old email, it would be up to the opposing counsel to argue that the person who made it made it for the purpose of fabricating evidence however many years ago.