If the God of the Bible didn't do what you think a real God would have done, that doesn't prove He doesn't exist; you might just be missing something.
It's the temptation of some who reject the reality of God's existence to use the following kind of reasoning as part of their evidence: "If the Christian God were real, He would [X]. However, He does not [X], therefore He is not real."
The problem with a person using this kind of reasoning is that he presumes to know what God would do, and often he does this without the proper knowledge of God's actions in the past, His character, or His overall purposes. The reasoning turns out to really be: "If I were God, I would do [X]. The Christian God does not do what I would do (in light of my purposes and goals), therefore He is not real." But God is a person. He has his own, specific goals and purposes. Because the reasoner's assumption is based on faulty understandings of these things about the Christian God, his prediction of what God "would do" is also faulty.
Some examples of this type of reasoning: "If Jesus had really come back from the dead, He would have started a revolt against the Romans." Or, "If Jesus had really physically risen from the dead, He would have stuck around instead of ascending to heaven." Or, "If God really existed, He would appear to everyone and prove He exists."
Matthew 27:39-43 gives another great example of this kind of objection:
And those passing by were hurling abuse at Him, wagging their heads and saying, "You who are going to destroy the temple and rebuild it in three days, save Yourself! If You are the Son of God, come down from the cross." In the same way the chief priests also, along with the scribes and elders, were mocking Him and saying, "He saved others; He cannot save Himself. He is the King of Israel; let Him now come down from the cross, and we will believe in Him. He trusts in God; let God rescue Him now, if He delights in Him; for He said, 'I am the Son of God.'"
Do you see the argument? "If you were really the Messiah, then God would rescue you from the cross. God is not saving you, therefore you are not the Messiah, and we will not believe in you." Since the survival of the Messiah (leading to a political revolt) was most important to these objectors, they assumed that this would be most important to God. But this conclusion was based on both a lack of knowledge and faulty assumptions about God's purposes. It turns out that the much better option for God was to not take Jesus down from the cross. They were completely wrong.
This story from Matthew might be a good one to bring up if your friend makes this type of argument. Try asking, "Would you be open to the idea that you're missing some information you need in order to understand what God would do in this situation, just as the people in this story were? I can see what's causing the confusion for you; so if you're interested, I'd love to talk more about this so I can help fill in the rest of the relevant details as you're trying to make sense of this."