The noise you describe is probably coming from the front drive line yoke splines at the transmission output shaft. It is very common that the wear in the splines causes “slop” that allows some “extra” rotation. When braking the vehicle, the drive shaft “holds” the transmission shaft back. When accelerating, the transmission output shaft “drives” the drive shaft in the opposite direction which allows the slop in the splines to rotate in the opposite direction and you hear this as a snap or bump. You can experiment to confirm this by letting the vehicle coast to a stop and then accelerating. There should be no noise. Then brake to a stop, and then accelerate. The noise should be present again. The harder the braking, the more pronounced the noise will be. The slop in differential gears will also contribute to this.
This is a very common in older/high mileage Chevrolet trucks, and my 1972 pickup has done this since 1976. Check the universal joints to confirm that they are in good shape and the play in the differential to confirm that it is okay. Otherwise, just keep driving and don’t worry about it. Take comfort in the fact that you know the answer the one of the great mysteries of Chevrolet trucks. Most owners wonder, but few know the reason. BTW, the symptom in my truck has never gotten any worse, just very predictable.