There are no rules for firearm noise levels.
There are simply no rules for this. Firearms are an afterthought in the Dungeon Master’s Guide, as there is a general expectation that most campaigns won’t feature them. Since there are no rules for firearm noise, there are no rules for reducing that noise. All of this is up to the DM.
It is worth mentioning that there really aren't any concrete rules for hearing anything, which nitsua60 explores in this answer, but apparently an official DM screen suggests a very loud noise is audible from 2d6 × 50 feet away.
Firearms are really loud.
I have experience using firearms, and have implemented them in a campaign once, DMing for a player using Matt Mercer’s Gunslinger fighter subclass. Our rule was basically “anything and everything can hear your gun”. They are just too loud to worry about making perception checks for anything. This means the suggestion from the DM screen mentioned above is unfortunately quite low. The distance from which a gun shot remains audible is typically measured in miles.
Movie silencers are fake.
We’re all familiar with sound of James Bond’s suppressed PPK, or at least, the sound movie producer’s like to use for suppressed firearms - somewhere between a whisper and a fart. It isn’t real. Suppressed firearms are still really loud. So even if your artificer could make a silencer as efficient as modern day suppressor technology, chances are you could still hear it from hundreds, even a thousand, yards away (small calibers such as .22lr can be remarkably quiet, however).