Glenn Peoples wrote an excellent post titled, "Do moral facts not require an explanation?" I highly recommend reading the post in its entirety. Here, I'm only posting one section on epistemological worry.
"If atheism is true, then we human beings evolved into what we are via a process that is now standardly described in textbooks on evolutionary biology, and crucially, they did so for no divinely appointed reason and with no creator’s plan involved. We developed as we did because this development was the path of least resistance. Changes occurred over the generations due to mutation, and some of those changes had the good luck to be more conducive to survival and reproduction, so those changes were kept, and on the process went. Now consider that while this process was going on, unguided, for millennia, there existed non-natural moral facts – facts that did not depend for their existence on any natural state of affairs whatsoever. While the most complex life on earth consisted of single celled organisms in a primordial slime puddle, these facts existed, and they continued to do so, unchanged, right through to the present day.
As a species, and as philosophers who think about ethics, we take ourselves to know some of the moral truths that are there – maybe even most of them. We have epistemic access to them. But supposing that the above scenario is correct, what are the chances that we should know any of those truths, let alone some or most of them?
Of course, atheists who reject the existence of moral facts have no problems discussing the origins of morality, since they are free to speak exclusively in terms of moral beliefs which are actually all false. In our developmental history our belief forming structures changed in ways that were beneficial to our forming beliefs beliefs that were useful for survival and reproduction, and we even formed sets of beliefs that we might call a “moral code,” but this has nothing to do with the truth of those beliefs. The beliefs were useful, and that is that. Their falsehood shouldn’t make us worried about holding them, as Nietzsche explained:
The falseness of an opinion is not for us any objection to it: it is here, perhaps, that our new language sounds most strangely. The question is, how far an opinion is life-furthering, life- preserving, species-preserving, perhaps species-rearing, and we are fundamentally inclined to maintain that the falsest opinions (to which the synthetic judgments a priori belong), are the most indispensable to us, that without a recognition of logical fictions, without a comparison of reality with the purely IMAGINED world of the absolute and immutable, without a constant counterfeiting of the world by means of numbers, man could not live—that the renunciation of false opinions would be a renunciation of life, a negation of life. TO RECOGNISE UNTRUTH AS A CONDITION OF LIFE; that is certainly to impugn the traditional ideas of value in a dangerous manner, and a philosophy which ventures to do so, has thereby alone placed itself beyond good and evil [emphasis original].8
If moral facts are not explained in terms of anything in the natural world, then there is, it seems to me, no reason to suppose that we would just happen to evolve as a species in such a way that we would find ourselves knowing what those facts are. Obviously (or so it seems, again, to me) if God exists then as a personal, albeit non-natural being, he might choose to let humanity know that he is there, whether by some sort of intervening revelation, or even by causing human beings to exist in such a way that when they function properly they are aware of his existence. But non-natural impersonal things like UMFs (unexplained moral facts) do not have this sort of ability simply because they are not personal.
If UMFs exist then, we have no reason to believe in them, or at least no reason to think that we are likely to know what they are."
You can read the whole post by clicking here.