I noticed the same noise and my Edge is only 8K old!.
I called the dealer service manager and they said it was common with the disc brakes during the first few stops.This is primarily due to the formation of trace corrosion (light rust) on the metal surfaces during vehicle non-use or storage. Supposedly the Edge uses a high iron content disc and it is SUPPOSED to do this. This corrosion is cleared from the metal surfaces after an few stops causing the noise to subside.
When you first drive off and then brake, you are scraping the rust coating off the disc and normal braking resumes- no grinding.
So for the time being, I am accepting this reasoning, but will have it checked during my free oil change at the dealer,
BTW, my pedal is firm and tight with no mushy feel.