I am fairly sure I already answered this question for you earlier. If not, then you can find a detailed response to this question in my book Is There a God
? which is available at www.ipibooks.com
But let me take another stab at this question.
How to prove to your atheist friend that evolution does not contradict God depends on your friend’s concept of God. Let me assume that he will let you define God for him, which makes sense, since he does not believe in God anyway. So let me define the question in these terms: How can I convince my atheist friend that evolution does not contradict what the Bible says about God?
Here is how you could proceed. What is it about the theory of evolution which is inconsistent with the belief in an all-powerful Creator? Unless we make certain presuppositions about that God, there is literally nothing about the existence of God which precludes that God using the natural process of evolution to create species. Presumably, from the perspective of theism, these natural laws were created by God in the first place. So, if God could create the natural laws which allow for evolution to happen, then what possible proof could there be from evolution that God cannot or even does not exist? I would argue that there is literally no rational reason whatsoever that the existence of evolution disproves the existence of God. The only way it could disprove it would be if we take as a starting point some particular assumption about God.
So… your idea of God, which is the God of the Bible, certainly does not preclude evolution. The God of the Bible is the creator of the universe and of the laws of that universe. God takes credit for creating all species, but the God of the Bible does not tell us HOW he did that creating. There certainly is room for the natural process we call evolution happening in a world governed by the God of the Bible. Of course, you are aware that some people take Genesis 1 literally and say that the universe is only several thousand years old, but this is one interpretation, and it is not even the most common interpretation of this creation story in Genesis. These “young earth creationists” do have a view which is a problem for evolution. That is for sure, but I believe that they are wrong. I believe that the “days” are not literal. I assume you do as well. If your atheist friend is assuming that the data supporting evolution contradicts the 6000 year old earth, you could simply give your hearty agreement to this statement and undermine the argument.
On the second question, what you need to do is convince your young earth creationist friend that he or she is wrong on the age of the earth. If your friend is able to reject his/her error of interpretation of Genesis 1, then the problem goes away. I believe that when God created the universe, he created it with natural laws which cause evolution to occur naturally. But this takes a lot of time. In a sense, God created evolution, so we might as well give him credit for his good work. God could create anything he wants any time he wants. If God wanted to, he could separately create 20 million different species. But the evidence is that he did not do this. I also am convinced that God created life. I also believe that God created Adam and Eve. However, I do not believe that anything in the Bible contradicts the theory of evolution. The Bible is not a science book. It is a God book. It is not designed to answer scientific questions, such as how God created various species. I personally believe that, like I said, God created life. I also believe that God intervened at times to move the process of evolution supernaturally in the direction he desired–that the process of change was not fully random (but I cannot prove this, by the way). Again, there is no reason for a Christian to reject the theory of evolution if they are willing to accept that the Genesis creation account is not a fully literal story–that the “days” represent periods of time or categories of what God did, rather than literal chronology. If your friend absolutely refuses to change his/her view of the young earth, then you will not be able to convince her/him that the theory of evolution does not contradict Genesis for the simple reason that evolution theory assumes deep time.