I am biological father of my daughter who is 6 years old.
My wife is not genetic((not carry, not her egg) mother of my daughter.
We used a woman overseas to be a surrogate as well as egg donor using IR procedure.
We did not adopt the child in US or anywhere.
She was born after our marriage.
Of course, we live in the same home since she was born.
If we go to court, what are my chance to get sole custody?
A child born during a marriage is presumed to be the legitimate and legal child of the parents who are married. Without an adoption, that presumption is rebuttable. However, the Georgia Supreme Court has recently ruled that the legal rights of a parent (in the case it was the father) cannot be terminated in a divorce case, but those legal rights must be terminated in Juvenile Court. If your wife's legal rights are not terminated, she has the same right to custody as you do. Your chance of getting sole custody is no greater than her chance to do the same. This is a very difficult area of the law, and is changing all the time. You need an experienced custody attorney to represent you, and one who will not be surprised by these changes.
You're in a huge legal grey area, as even though Georgia presumes you and your wife are the parents, that presumption can be rebutted by medical evidence, meaning other people outside the marriage could claim parental rights, albeit unlikely. In a normal situation, odds are you and your wife both have a chance at custody, and given that sole custodyu absent parental misconduct is rare, your desire may be very different than the result.
Regardless you need a good lawyer if a divorce is planned.