Origin or SimCity may not have registered yet. You do have to open it while online & let it register to play the first time. It will always say you're offline & to log in for all features, but that shouldn't prevent you from playing.
Can you get to the SimCity launch screen? There should be 2 tabs above the play button. It defaults to Multiplayer, you need to click on the tab that says Single Player. I can't seem to upload a picture here, only have access to my cell. Here's a video that shows how to do it https://youtu.be/vKdcq-pzRBg
If this doesn't work, try clearing Origin cache and logging back in to force the registration. https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/