Wow. Here are the questions. Got answers?
"What legal avenues do we have if it can be proven that a public school teacher is arguing in favor of atheism ( the denial of God) in a classroom setting?" As a follow-up to that question:
" What manner of proof would be needed?"
I don't see that there are any LEGAL avenues to pursue, yet. It is unclear that the teacher is doing anything unlawful. Arguably, he is trying to foster discussion of differing ideas.
I think I mentioned some time back the avenues you must look at, first. The student's GUARDIAN (if that's you, great, if not, then THEY need to do this) can ask to meet with the teacher and discuss the issue. If you or they are not satisfied with the response, they may then meet with the school administration. If they are still not satisfied, perhaps they can ask to transfer him to a different class. From what you have thus far written, I don't know if there is anywhere near sufficient grounds to SUE anyone or take any other legal action.
Keep in mind that I am speaking to you as one who believes in the Bible, is an evangelical Christian, has had four sons survive public school, and also teaches high school (and my wife teaches elementary school). There are a great many challenges to people of faith within the public school system (particularly in CA), and I have had to fight that battle a couple of times over the years. But, each such "fight" was relatively easy and they were each resolved with a polite conversation and non-confrontational meeting with a teacher or an administrator.
Don't go looking for a lawsuit just yet. His actions may well be perfectly lawful, and may well be capable of being addressed with a meeting or a transfer to another class. If your grandson is going to function in a secular world that is often hostile to believers, he will need to learn to navigate such discussion and debate - even open hostility. He will survive this just fine.