You'd probably be a lot better off not suppressing the gun, but picking a shooting location and taking steps to contain and muffle the blast.
I've seen various plans/write ups from people who have built small shooting shelters that are lined with sound absorbing materials like carpet and foam, and others who have built "shooting tubes" out of tires or large pipe that is similarly lined.
It won't completely deal with the noise, but it will sufficiently muffle it to the point where it might not bother your neighbors.
Here's a good discussion from Shooters Forum from some years ago on the subject.
https://www.shootersforum.com/genera...nge-noise.html