Have you tried decreasing power and/or increasing speed?
Some materials do not darken well. Wood has a nice long linear region where as the laser energy is absorbed it gradually turns darker. Paper is not so generous - the material absorbs energy doing nothing for a while, then rapidly blackens and burns. Finding speed and power to burn a grayscale image onto paper is very difficult compared to wood, it’s sensitive to small changes.
The thickness of the material is not particularly important except for cutting. Engraving only affects the top of the material (within a reasonable heat affected zone).
It looks like Snapmaker’s demo was on a heavy canvas.
Whatever material you’re using you will need to perform a series of power and speed tests to identify where the material begins to darken, and when it reaches the black point you desire.
Hypothetically, let’s say at 300mm/min it begins to darken at 15% power and is dark enough at 50% power. Those settings would then be entered in software.
To come up with those settings you would need a power test grid and run at various speeds. Various people in here have their own methods for determining power and speed, I’m sure the search can locate some of them.