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