If I want to engrave Proofgrade maple plywood to 1/2 its thickness to make a lap joint, I do 340 lpi, 700 speed and 60% power at 3 passes. That makes four variables to control for very specific effect of having an even surface and not having a real bad char to clean off, plus a little more out of the depth to ensure that nothing stands proud (which is important to the design of the little roll stamp box I made).
I discovered this by many test engraves, which I had to do three times with pre-release power profile changes and then to final production unit.
Your needs may require something else, but this is what works for me that I can rely on.
So to re-iterate, the laser can’t know it has cut through deep enough. You have to do some tests to see. I did quite a few on some .43" acrylic to see how depth works and what happens on successive passes. Learned a lot for that.
Cardboard was a fun test to, especially depending on the design, and the orientation of the corrugations, it behaved differently. but what is cool is engrave the top layer off of cardboard and leaving the corrugations intact as a design element.
Start at highest speed and lowest power (which seems to automatically get filled in for non PG materials when choosing an operation. Then test by changing one variable.