Cross project management using service account

Question

I need a service account that can access multiple projects, but I have not been able to find a way to do this at all. It seems that a service account is always bound to a project.

Another option is to create a service account on the separate projects and then authenticate them using gcloud auth activate-service-account --key-file SOME_FILE.json, but the problem here is that it does not seem possible to automate the creation of service accounts.

So the question is then: Is it possible to create a cross project service account or to automate the creation of a service accounts? Even better would be if I could do both