Very common problem.
I think you'll find that it's the run/start capacitor. Easy and cheap fix. About $12 for new capacitor on Amazon and maybe 15 minutes of time.
Watch the replacement on this video below.
Run start capacitor replacement - Google Search
A post here reminded me. The Carrier systems have (last I knew) a 5 year warranty parts and labor, 10 year parts only.
When my system did the same as yours, I spun the fan manually with a long screwdriver to get it going. It cooled the house fine until it was time to restart. Service technician was angry that I did that as he said could cause the fan motor to burn out. All is well after a couple of years. I keep a spare capacitor now for the next time.