If the beam is square, you will get the same witness marks with the head positioned at each of the four corners. The process in the documentation describes how to make it square: You measure by shooting the laser, moving the gantry/head, and shooting again, and looking at the witness marks.
From one of our Lasers > Getting Started with CO2 Lasers articles:
Note that if the third mirror does not align the beam with the middle of the lens, the beam will not be focused correctly and will not be aligned with the hole in the nozzle. You may wish to use a device that helps you align using a red visible laser. […] a tool used only while performing alignment
This allows you to work backwards from the head using a visible laser beam. It might be substantially less frustrating for you.