If my son's father isn't on the birth certificate do I still have to take him to court in order to get sole custody?

If there has been no filing to establish paternity new presumptively have sole custody and may be making things more difficult for yourself by filing.

I am unclear from your question whether you were married to the father. If you were not, then you do not need to file for custody in Georgia. I note that you live in California and each state is slightly different. I would suggest you consult with a competent family law attorney to determine your options regarding custody, visitation and child support. A good consultation may save you time, money and headaches in the future.

Why? What makes you think you need to get court orders for sole custody? Is the father in your son's life? Is he trying to get custody? Has paternity been established?