The bullet is out of the barrel completely before the gas system charges (the rifle actually operates on residual pressure). However, the suppressor slows the rate at which the rifle vents- that's one of the ways it reduces the sound. Because of this, pressure is higher so more gas flows through the port bringing the expansion chamber up to operating pressure quicker and increases carrier acceleration.
It also means that there is more gas being dumped overboard through the carrier vents and more gas from the gas tube after the gas key separates from it. This results in more gas to the face.
While a heavier buffer will slow the carrier acceleration, it does nothing to reduce the volume of gas venting from the carrier and gas tube. To do that, you need to reduce flow from the gas port. That means either changing to a barrel with a smaller gas port or getting an adjustable gas block