The brakes on my 2007 LaCrosse do not feel like they are engaging when I am reversing and the car is cold (first thing in the morning or first thing after work). The pedal feels very stiff/hard and the car doesn’t feel like the brakes are stopping it. Every time I apply the brakes after that first time, they behave fine. I had the front brakes repaired/replaced but the problem persists.
Could be related to the brake booster. Try pumping the brakes before starting the car. Nothing crazy but you’ll likely find it becomes/is very stiff. Hold your foot on the brake and then see if it goes down after you start the car. It should move down some. If it doesn’t, you may have a vacuum leak to the brake booster or the booster has a problem.
If your brakes feel mushy, I would look into getting them bled but they feel normal, after that first time, I take it?
It’s your brake booster. It’s supposed to hold one “charge” of vacuum for just this reason, but it seems your vacuum charge is leaking out (or in, lol.) Have you ever noticed that once you turn a car off you can still hit the brakes “one more time” before it gets hard? That’s the “vacuum reserve.”