Same issue with my 2019 Silverado 2500, and iPhone 11 running iOS 13.1.2. I got an iPhone cable directly from Apple, formatted my phone like it's brand new, and began my testing.
With my freshly formatted iPhone I would simulate my typical drive cycle. So unlock the car with the remote, open the door, close it, start it up, plug in my iPhone, check to see if it works or not by waiting a minute or two and pressing the projection button, and then turn the truck off, take the keys out of the ignition, open and close the door, lock it with the remote, and repeat.
Out of 10 or so times I've tried, it only connected two or three times and only using the USB ports directly under the infotainment system. CarPlay did not start up at all for me using the USB ports in the arm rest cubby. It also did not start up for me using an Amazon Prime iPhone cable.
Here's the video - https://www.youtube.com/watch?v=uAjVRdZH398