If free will doesn’t exist, and we live in a deterministic world, our choices are arbitrary. If they are choices at all. Any decision considered ‘good’ is simply what was going to happen anyways.
If free will does exist, we have the ability to make meaningful decisions. But for there to be good or bad, there needs to be a standard. If there is no standard, the morality of the decisions is subjective. And therefore, is arbitrary.
If free will does exist, and there is an objective moral standard outside of God, we still need a reason to act a certain way. Why is someone who acts with the well-being of others in mind better than someone who prefers that others suffer?
If you only do good things to be perceived as good, are the things good? The intent matters. So to do it because it feels good is no better position. It’s like telling your kids that they shouldn’t do something because you said so.
Essentially, in morality 2+2=4. Some people say there are no numbers. Some people say that it can equal whatever you want. Some people say that it does equal four. But those people cannot reproduce the method. It’s right because it’s right. And you should do it because it is right.
So if intent matters in an act, and if objective good needs a standard, you can’t be good without God.