Hello!
My 2004 Pontiac GrandAm has a braking issue where upon startup the brake pedal is often smooth, soft, and brakes normally… but after a few miles of driving the pedal becomes very firm, sensitive, and my brakes eventually ‘lock up’ to the point of burning due to friction and seizing. Turning the car off for a few hours often allows the brakes enough time to slowly release, and go back to ‘normal.’
In the past year I’ve replaced Drums, Shoes, Pads, Calipers, Brake Hoses, Rotors, and Master Cylinder with all new parts but can’t get the issue to resolve.
A recent inspection found my caliper to be slightly dented or damaged, likely due to this braking issue as all parts were replaced with brand new parts. All past inspections found my caliper to be seized.
Your brake booster is probably going bad. It's the large black cylinder on the firewall in front of the driver, the master cylinder bolts to it.
Your vehicle has an ABS braking system. When replacing parts and refilling and bleeding the system of air, a fairly sophisticated scan tool has to be used to set the brake control solenoids in the proper position to bleed the system. Otherwise, it will not work properly. And, like @justin-shepherd indicated, check for proper function of the brake booster diaphragm and any vacuum leaks between the intake manifold and the booster.