Ok, that makes sense
There will not be any suction during blow down as the system is pressurized. That's why the gases are venting. The easiest route is the one that offers the least resistance.
After the bullet exits, the gases of course vent out the muzzle. After the bullet clears the bore and suppressor, the BCG finally pressurizes enough to begin extraction which unseals the chamber and what's left of the gases begin venting in that direction
The pressure drops as the bullet travels down the bore because the volume is expanding and I think gas temperature is dropping. Pressure will continue to drop as the gases fill the larger volume of the suppressor
Of course there is gas in the bore & suppressor before the rifle is fired. we are not shooting in a vacuum
. Also, the bullet does not seal the bore perfectly so some of the gases will leak past the bullet as it's pushed.
The gas is expanding at approximately 5,700 fps. Of course, while in the bore, the gas cannot expand faster than the bullet allows. That's how the pressure is built up. Once the bullet uncorks the muzzle, the gases overtake the bullet. (That's why a good crown is so important to accuracy.) This gas passing the bullet is a large part of the puff of smoke seen ahead of the bullet in the slow motion videos