If God did not create then there would be no evil. But He is a Creator by nature and His plan for all creation is greater than the existence of evil that comes from His creation rejecting Him and being separated from Him. He did not create evil. He said all He created was good. Sin entered into all creation by Adam’s sin. But even before that happened in our time, God had already purposed Jesus’ redemption in time for all mankind. He already saw the beginning from the end. It wasn’t a huge “oh, no, what have I done.” He knew all that would happen before He spoke a single thing into existence. And He sees the glory of all creation that comes through Christ and is being revealed in time. The glory of creation and of the Church being made ready as heir with Christ for all eternity far exceeds anything evil that can be brought about in this earth before evil is banished from creation.
Now is it evil for God who created a life to take a life? Life belongs to Him. He’s the author and giver of life. Life does not belong to us. It is wrong for us to take a life. It is not the same thing for God to do it. God sees the beginning from the end. He is God. Do we have cause to judge God as doing something wrong in bringing the Flood to wipe out a perverse generation and saving Noah and His family who serve Him? God’s justice was brought forth with the Flood. God’s justice was also brought forth by saving Noah.
If God does not exist, the whole discussion about good and evil and if God is good is a moot point. But if He does then the only way we know what good and evil are is because He revealed that knowledge to us and the self-sustaining self-evident God is the only standard of all holiness and righteousness.
Good and evil exist and we know the difference between them because there exists a Good God.
Also regarding suffering: see Peter Kreeft's essay.