Jenkins: make a credential available to all users
I was a little confused by the OP question and follow up, so answering about GitHub access to jenkinsfile-based pipeline jobs:
Credentials stored in Jenkins can be available to all users with rights to create jobs. Use a GitHub deployment key for your repo. Yes you need a key for every repo. This does require a user in Github, of course, but there is nothing to stop you from paying for an extra so-called 'machine user.' We, however, just use a real person like me.

This GitHub deploy key allows you to trigger on repo changes, or keep your jenkinsfile in Github. Using jenkinsfiles and keeping them in GitHub, is the best way to do Jenkins, I think.