I have created a YouTube API key, but when I try to use it I get an error message that the key is not enabled. When I try to enable the key in the Google Cloud Console, I get the error message:
IAM: you have insufficient permissions to enable or disable services and APIs for this project. Contact a project owner to request permissions.
I can't seem to find a way to set the project owner. I created this project myself, so I should be the project owner. I'm not sure if it's relevant, but the account is managed via G-Suite.
Update: per the documentation, I logged on to G-Suite as an administrator and went to Apps > Additional Google services, but "Web & App Activity" is not listed as an option.
Your gsuite admin can activate the API or remove a restriction on it.