Except the wording of the 14th Amendment doesn't REQUIRE a trial.
No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.
Now, in some ways, this is kind of dubious, and even at the time, it wasn't enforced.
The only non-Civil War application of this clause was when a German-American Socialist congressman from Wisconsin was tried for "espionage" for opposing war against Germany in WWI. The Supreme Court struck it down and he was returned to his seat in 1922.
All that said, I'm all for filing these actions in every state possible. Not only to make Trump burn up his resources fighting them, but to remind everyone what this guy did.