Let's get back to the OP, with perhaps some clarification. Most of the religions we know about have been moth-balled. Only a relatively few have substantial members today. The OP is concerning claims made by religious folk - in these modern times - that they are the holders of the moral high ground because their morals come from their god. The "revelations" from the gods that are all the rage today are well within the bounds of history. For example, we have plenty of historical evidence of times before any of the Abrahamic scriptures. So, if say an early Egyptian god revealed some morality, that would would predate an Abrahamic god's claim to that moral truth. Put another way and by example, the 10 commandments merely codified a bit of the well known, pre-existing morality of the day (and tacked on some weird stuff, but that's another discussion).
So I agree, the origins of morality are murky at best. But what we know for sure is that they weren't originally revealed by a modern god.
I feel like this has become a very different sort of claim, though I guess it is hardly news for an atheist on this forum to say "religion" and mean "some if not all conservative Christians", despite RF's many fine polytheist, animist, and liberal theist posters.
But even with the revision, some of your basic problems are still there. One is that the oldest traditions have spanned the whole of written history, and indeed most of our earliest texts are "religious", with modern devotees no less. It seems likely that there were religious echelons that predate these early foundations, but we don't actually know that, and could not reasonably decide whether the chicken or the egg came first, in an exceedingly murky prehistory almost certainly populated by folks who saw no distinction between religious and secular sources of authority. Even more recent religious movements ultimately lay claim to earlier texts such as the Vedas or Hebrew Scriptures, before the creation of which we have little in the way of a detailed record.
Another is that you are conflating specific forms of religion such as texts and modern labels with the monotheistic claim that morality comes from God. By which I mean, I don't think when a Christian or Muslim says that morality comes from God, they don't actually mean that it comes from the Bible or the Qur'an, they are serious about it coming from God. Which means that proving that a thing existed before a given book entered history doesn't affect their basic claim. The books are there to give moral advice (and in this role they are very important) but they don't create the thing they describe. Muslims in particular maintain that although the Qur'an was the last and greatest warning, it preaches the exact same Message that has always been preached by true Prophets. You can read the Bible this way too, though being an anthology, it talks less about itself.
So I'm not sure your invisible opponents would be likely to make the claim you're trying to oppose in quite the way you are putting it. God, not religion, is the source or morality. And
He is not, presumably, predated by anything. Unless the claim of his existence and nature is entirely false. Conservatives
do get very upset by conversations about given passages in other cultures' texts predating their inclusion in Scripture, but that isn't specifically why.