You don't have the folder yet because the game doesn't get that far into generating it.
Tells us which of these 3 happens.
You press play. Launcher closes, no image appears on the desktop and there is no process in task manager
You press play. Launcher closes, no image appears on the desktop and there is a process in task manager for archeage.exe
You press play. Launcher closes, an image of a poem appears. It disappears before all the text can light up
So it does do of them. It does the first one.
This happens only when something is preventing the game from launcher or outright terminating the launcher process.
The things that cause it are not running the game as admin
Not setting anti virus exclusions correctly. (Post your exceptions list)
Fault within the installation. Give you've reinstalled multiple times we can rule that one out.
The splash poem crashes are different for each stage of the poem it reaches. So there is no 1 solution to everything.
I am going to assume for this case you're asking about a crash on the first line 3rd word in.
This occurs when the game can't allocate its virtual memory. Unfortunately this is not a simple thing to fix as to go through and fix the issue manually is too complex for the common user and will cause more problems for the person if a pc restart isn't enough to get it working.
Its for that reason the easiest way to resolve it is clearing off the game and reinstalling.