CarPlay is supported on your e-Golf:
CarPlay is supported on your iPhone/iOS version (iPhone 5 or greater, iOS 7.1 or greater).
So neither your car nor phone is the issue.
The e-Golf uses a 'hard wire' integration. It does not support wireless CarPlay. So before heading off to the dealer, you might want to be certain you're connecting your iPhone to the USB port located in the cubby under the infotainment unit. Second, be certain you're USB cable is not the issue. I had a been using a cheap lightning cable that only worked when inserted into the phone one way, but not the other. I swapped the cable for a real Apple cable and it worked just fine. Not wanting a white cable in the car, I had located a short black lightning cable and it worked just fine too. I'm still using this cable.
If after confirming you're connected to USB with a good cable and it still doesn't work, then consider reaching out to the dealer for assistance.
Hope you find this helpful.