If you live in this world and you try to make sense of the fact that there cant be real justice found and you are atheistic. That is a big problem. I guess this question cant be important for most of the atheists? For according to their materialistic world view it wont be any compensation for suffering that is unjust and no punishment for the ones that the law cant catch. Someone born into poverty , slavery or war the list can be made much longer of coarse. So if there is no afterlife where a judge that everyone has to face can judge each and everyone of us by how we have lived. And if there is no compensation for the ones that have suffered unjustly then this world falls out of the realms of true understanding or at least out of making sense.
What happens when you as a person cant find justice? Then you start to doubt and then you start to question things. Of course can you then start to live at least your life more justly but according to what standards? We can turn a blind eye to things in this world but only to a certain point. Remember that a sense of justice correlates with a sense of meaning. A person living in drug abuse and criminality have very low meaning by their own subjective standards in life but also according to more inter subjectively definitions. And someone running a hospital in a poor country have high subjective meaning in life and will also be seen upon as someone with a higher sense of meaning. But we face things that are also out of the realms of justice. If we just ignore these they wont disappear no they will dwell in our subconscious and over the years that pass they will build up within to such a grade that they will manifest into a depression or something else. So by looking at one way that atheism can go is by pure nihilism. We can read about the mental health of the philosophizer Friedrich Nietzshe so that doesn’t seem to work. If you kill God and all moral law is being set to nihilistic standards then you surely will dwell in pure meaninglessness.
But if there is a God then there can be meaning through justice and through compensation beyond our imagination for the ones treated unjustly in this life. And then we can rest in our faith when we face evil in this world. Or simply be reminded of the limits of man. We can add to this the realm of the transcendent justice in the one and only good, the creator and law giver, our objective true justice , God!