I'm having the same issue!!! I have taken it to the dealer 3 times and the most recent they had it three days and couldn't recreate it. I got my Sonic home and 30 mins later, used the remote start and sure enough there it was! I'm livid!!
It's more like a loud rattle right as it turns over towards the engine of the car. Not rear. Just for a brief second. Only when starting after it hasn't been ran/driven for 30-45 mins or more. It doesn't happen twice in a row either. It's not the "ticking" as the dealer calls it from the chains, it's in addition to that. I can start it in the am and it does it, 9 hrs later after I'm off work I remote start it, it does it, then maybe go to the store and spend an hour grocery shopping, come out and remote start and... yep you guessed it, it does it. They said they checked the exhaust pipes and muffler and nothing loose. Which concerns me more, if true. I'm at a loss now. I had a loaner for a few days, which was also a sonic and when remote starting that car at cold start it didn't do it at all and sounded normal. So I know it's something with my sonic. I don't know what else to do either...... I've had the problem for 9 months now. EVERYDAY! Ugh....