The trial in U.S. District Court is expected to last four days.
The lawsuit argues that the disclaimer restricts the teaching of evolution, promotes the teaching of creationism and discriminates against particular religions.
County school officials said their warning, in the form of stickers inserted in science books, simply encourages students to keep an open mind.
The stickers read: "This textbook contains material on evolution. Evolution is a theory, not a fact, regarding the origin of living things. This material should be approached with an open mind, studied carefully and critically considered."
The lawsuit was filed by six parents and the Georgia chapter of the American Civil Liberties Union.
"I'm a strong advocate for the separation of church and state," said one of the parents, Jeffrey Selman. "I have no problem with anybody's religious beliefs. I just want an adequate educational system."
The school board adopted the disclaimer after three science texts it adopted in 2002 were criticized by some parents for presenting evolution as fact. More than 2,000 people signed a petition opposing the biology texts because they did not discuss alternative theories, including creationism.
A lawyer for Cobb County schools, Linwood Gunn, said he expects the disclaimer will hold up in court.
He said the stickers "improve the curriculum while also promoting an attitude of tolerance for those that have different religious beliefs."
The U.S. Supreme Court ruled in 1987 that creationism was a religious belief that could not be taught in public schools along with evolution.
In April, U.S. District Judge Clarence Cooper refused to dismiss the lawsuit, saying the school district's disclaimers could have the effect of advancing or inhibiting religion.
The judge applied a test handed down by the U.S. Supreme Court in 1971. In order to get the lawsuit dismissed, the school board had to show that the disclaimer was adopted with a secular purpose, that its primary effect neither advances nor inhibits religion, and that it does not result in an excessive entanglement of government with religion.
Cooper said the school board satisfied him only on the first issue.