I’m sorry but that’s not right. The sound of the power igniting is next to nothing. The mechanical action of the gun cycling is almost as loud in many cases. All of the boom is the sonic boom when the escaping bullet and gases break the sound barrier.

To “silence” a gunshot you do two things. You can use subsonic ammunition so that the bullet does not break the sound barrier. A suppressor on the end of the barrel has exactly one function, it slows the speed of the escaping gas to below the speed of sound. You can fire regular supersonic ammo and the suppressor will help a little by removing the boom from the gases but you’ll still have then smaller sonic boom from the bullet itself, in that case.