It's a little difficult to show without some graphs, but the only way peak pressure could occur before the bullet moves is if the propellant burned instantaneously. And that does not happen. The peak and decline pressure curve shape depends upon the relative quickness of the propellant. Assuming identical muzzle velocities, the pressure from a load with a propellant of high relative quickness will peak early and decline rapidly. The pressure curve from a propellant having a lower relative quickness will peak later (and lower) and decline more slowly.

Those who understand calculus may be interested to know that so long as the bullet weight and muzzle velocity are constant, the area under the pressure-time curve (its integral) must be the same for propellants having differing relative quickness. But the curve shapes will be different.