Hey, GitHub doesn’t have phone support but you can send over a message to them here: GitHub Support
On the other hand, I am a human, perhaps posting your question here might resolve it faster. Let me know if I can help and happy new year!
Github Support
how to contact customer support about billing?
Does github have any other way for example a toll free number, socials or anything else where to contact them other than their painfully slow ticketing system for time sensitive stuff?
You can contact a GitHub user by going to her/his user page (https://github.com/[USERNAME]) and on the left-hand side, you should see her/his email address if they have provided one. Also, make sure you are currently logged in, otherwise, it might not be visible to you).
Check out the repository and look for their email address in the Git log.