Evil is not eternal in the way that God is eternal. It’s not an equal, opposing force or substance. All things are within God’s Providence, including evil.
Two of the greatest theologians in western Christendom are Saint Augustine of Hippo and Saint Thomas Aquinas. Both taught that evil is an absence, a privation of goodness in something that exists. It is not a positively existing thing in itself. The idea is based in an essentialist view of reality, not an existentialist view. As an illustration, consider the ideal mathematical, equilateral triangle. Now imagine that triangle drawn by a six year old with a crayon. The triangle drawn by the child will still be a triangle but it will be defective. It will be deprived of perfections that make it a good triangle, for a six year old cannot draw straight, and a crayon is a poor tool for making straight lines. Now consider a triangle drawn by an architect with a straight edge. This will more closely resemble the mathematical, ideal triangle, but even so, it will still be imperfect, because even the line drawn by the sharpest pen will still, if examined closely enough, not have perfectly straight edges. But it will be less deprived of what it is to be a triangle than the one drawn with a crayon.
Now, these privations in a triangle are not moral evils, but the concept is the same. Evils done to a human person are things that deprive him of some essential quality of being human. Evil choices made by a human are evil because they are deviations away from how a human being should morally choose.
Evil is not a consequence of God’s existence per se, but it is something He chose to permit in creation. In this essentialist view, you couldn’t have either change, variation, multiplicity, or choice in a reality in which evil wasn’t permitted. Evil isn’t just moral choices, but any deviation in reality away from the essence of what a thing is; it’s ideal; it’s “blueprint” of what it is.
Though I should add, God may have had other or additional reasons for permitting evil.