To specifically answer your question, they exist as subjective concepts like the concept of the number 1. By subjective I mean that they only exists in minds capable of understanding those concepts. If there is an apple on the ground, a mind may think that there is one apple. This happens because the mind in question compared the definition of the number 1 to the apple. The apple doesn’t somehow embody the concept of the number one.
The concept of the number 1, like good and evil, doesn’t objectively exist somewhere. You can test if something is objective or not by theoretically removing all minds. If you remove all minds who understand what a $20 bill then all is left is a piece of paper with some ink on it. The piece of paper being worth $20 and the meaning of the text and numbers on it are all subjective. These are sometimes called shared fallacies, like American soil, this computer is mine, there are 5 cats, etc. Subjective ideas are only useful when they can be properly mapped to objective reality (using definitions) and other minds also know what they are.
God existing or not existing does not affect these concepts being subjective. I can explain this further if needed, but a god could only claim some form of moral authority over good an evil. That is why others are asking about definitions here because they matter a lot when talking about subjective concepts. For example, the Bible will say things are evil, but never say why, or more importantly, what the full definition of evil is.
This is a good question. Discussion on subjective topics are both interesting and can be helpful. Good and evil are extremes and there is a lot of middle ground here that ethics also covers. Personally, I would consider a poor single mom stealing something to feed her kids, maybe not good, but definitely not evil. A rich person stealing to get themselves richer I would consider to be evil. Once again, those are my definitions and having discussions to see what others use for definitions and why they use them is worthwhile. The goal isn’t to try to create some list of good and evil for some draconian purpose, but to improve ethics to help advance us as a species.
There are two mistakes that theists make here. First is that somehow good and evil existing means that their god exists. This is just another post hoc ergo propter hoc fallacy (assuming the source). It is also quite circular: “We know good and evil exits because of god, we know god exists because good and evil exist.” The second is that we should assume the moral authority of god exists when we can’t prove that god exists in the first place. If people made up god and religion, then they made up the underlying ethics too, there is no way around that. Therefore, it makes no sense to believe in some religion’s morality if there is no evidence of it being true. In ancient Mesopotamia religions, which Judaism is a branch, they would claim their moral rules, aka good and evil, were true because the god they believed in said so. That’s nice and all, but without evidence of this, I’m going to assume it is just another person’s rules with really weak justification.