I have a 2006 silverado standard work truck that just recently turned 100,000 miles. I just replaced both front calipers. I bleed both sides and did not notice any air bubbles but I do not have a firm pedal. So I went to bleed the rear brakes and in doing so I notice not a lot of fulid to the rear brakes. The front calipers definitely needed to be replaced but now I'm thinking it's a bigger issue somewhere else. My truck has rear drums and honestly not sure if it has a ABS system
I am not mechanically strong but I do know some basics, but this is frustrating

 

First, make sure you installed the calipers on the correct side and in the correct orientation with the bleeder screw on the top side of the caliper. Second, hit the caliper with a rubber mallet to loosen any trapped air.

Your 2006 Silverado likely does have ABS. You can do a "quick and dirty" ABS activation by getting up to speed on a gravel road or in a parking lot and then slam on the brakes to force the ABS unit to cycle, then go home and bleed all the brakes again in case you dislodged trapped air.

Good Luck!

 

If you can't find anything hydraulically wrong,,,,,,,,,if the rotors were tapered a lot when the new pads contact the rotor it may be partial contact and addl pressure on the pedal causes the pad to flex enough to produce a soft pedal. What did the old pads show as far as thickness at top and thickness at the bottom of the pad?

Did you have the rotors cut or replaced?