Same, I have received a stadia controller as a gift this morning. The purchaser didn't receive a code either. It was ordered on the 14th Dec. It was just the controller not the ”founders edition” as I already have a chromecast ultra. There's no mention of invite codes anywhere if you just buy a controller.
Codes are only given with Founders Edition or Premium Edition bundles. You don't receive a code just for buying a controller. Base edition will be launched in early 2020 where you can get access to Stadia without having Founders or Premium edition bundles. Alternatively, if you can get a buddy code then you can access with or without purchasing a controller.
I would suggest reaching out to Google support and raising the matter with them. You should normally receive the activation code very soon after receiving the CCU and controller. If it has been more than a day since you received the premium package then raise it with the Google support team.