timppu: It mentions e.g. /silent and /verysilent options, which I presume should do what you are looking for.
rtcvb32: I was sure those were for error messages and the like...
I have no idea, the description just says "Instruct the setup to be silent or very silent.". There are also the other options but when I tried them (like /SUPPRESSMSGBOXES), I didn't really see how they changed anything, the setup seemed to run normally, with ads. This lead me to believe that maybe these options aren't supported anymore in the newest installer versions?
The /SILENT and /VERYSILENT options did make the installer silent, but then the installer didn't seem to even launch at all, like exiting without any message. I waited for some time whether it is installing something in the background, but nothing seemed to happen, the game didn't appear at least in the default location etc.
I seem to recall seeing discussion about this before, how to install GOG games from a command prompt without needing further clicks and selections from the user. Jmich maybe?
...
Ok, I did some more testing, with an older installer (setup_7th_legion_2.0.0.5.exe). With it, /SILENT option disabled all the other prompts etc., BUT shows the ads. /VERYSILENT doesn't even show the ads, so it does what the OP wants (it seems to show absolutely nothing, the game just gets installed in the background).
So, to me it seems the options like /SILENT and /VERYSILENT may work with older GOG game installers, but maybe not the newest ones (which have the new versioning scheme etc., like A Bird's Story). It could be these options are now disabled as the new installers (non-classic) have also an extra option whether or not to install GOG Galaxy, and maybe they didn't feel like adding yet another extra option for that for the command prompt installation etc.?
Or then I simply didn't know how to use them properly with a new installer, as it needs those "" around the installer filename etc...?