Before you start the car you have no vacuum, which means the brake booster isn't working. That's why the pedal firms up, and then softens after you start the car. What you're describing sounds like normal operation.
I have about 600 miles on my GTI w/DSG and notice the brake pedal anomaly you're talking about. It's not the system, in my case, it's something with the pedal action itself that causes it to catch a little bit. It doesn't bother me, but it could be something simple to fix.