Welcome to the forum. I'm certainly no expert, but how old is your battery? My car was starting fine, no problems at all until I had my A/C looked at. They replaced my duct temperature sensor, which ended up not being the problem- it was the HVAC control module. After receiving my car back, overnight, it would default the DIC to the vehicle mileage (I always leave it on instant fuel economy, and before this, it would be right there on that setting when I started my car) and it would erase the parameters for average mileage, fuel used, etc. It did this for a couple of days, and I assumed it was related to my duct sensor. I should note that as a work around for the HVAC control module, they left the duct sensor unplugged and as a result, the A/C was blowing at 32 degrees with ambient temperature being 61.
However, I remember reading that a dying battery will have weird results on a Traverse, and it was a Saturday (shop was closed that did the A/C work), so I decided to look at my battery. When I took the battery out, it was the original battery. Manufacture date was August, 2011 and my traverse is a 2012. New battery at Costco and the DIC worked perfectly again. Also, it cranks much faster. I just didn't know any better regarding the cranking as it was what I was used to.
Long story short, I would check your battery. I found my battery going dead to be SUCH a coincidence in timing since I just had the car worked on, but I'm glad I checked it out. Also, my A/C was flashing 3 times some of the time, and others it would stay lit but the recirculate button wouldn't work while on the dash air setting (blowing at your face). In my case, it was a failing HVAC control module fooling the car to turn off the A/C because it doesn't know what temperature it is outside. I ordered a new control module and will be replacing it soon, and trying to figure out how to re plug in the duct sensor. I hope this helps, but like I said, I'm no expert.