I had this same problem briefly where my dlc cars didn't show up after playing in offline mode, I play on PC and instead of starting it from the desktop shortcut I went into my origin account and started it up from there, apparently my local and cloud saves weren't synced and that worked, hope this helped
I know exactly the problem you are talking about. I've spent hours trying to figure it out. I've contacted steam, origin, and ea and none of them could help me. I thought the problem had been resolved, but it showed up again after a while. After reading this reply, I closed the game and made sure both origin and steam were logged in and open, and then started the game from origin. I did have it set to single player when I closed it because I found that I could use the cars in that setting while connected to internet.
