When reading Ainulindale, the common opinion seems to be that the excerpt is Tolkien’s version of Genesis. It is a myth, written in biblical style, about the creation of the world. It features God conceptualizing mankind and sending beings akin to angels down to Arda to ready the world for the arrival of His children. And yet, Tolkien adamantly denied the allegorical nature of any of his works. If Ainulindale was really meant to be the Elven Genesis, such a denial seems rather pointless. Writing a creation myth that shadows another one would almost have to be allegorical. Because of this, it seems that Genesis is really the wrong thing to compare the Elven myth to. Tolkien’s work was full of Christian ideals and symbols, but I would hesitate to assert that the work was written in a Christian style. Instead, Ainulindale seems to be written in a style drawing from other ancient mythologies, where their themes are almost more prominent than Christian ones.
The most striking aspect of Ainulindale is that there is not one creator. While Illuvatar was the one who created the Ainur, he was not the one to spin the Music. Nor was he the one to sculpt the world, an act done later on by the Ainur. Instead he serves as the father of the Ainur, and as their guide. Rather than create his own music, he has his aspects do it for him. His only role is to set a theme, a guideline that the Ainur are encouraged to follow. They aren’t actually bound to this theme, as Melkor demonstrates, and in the end all Illuvatar can do is set a new theme for the Ainur to follow. Whether he could have done anything about Melkor is unexplained, but the fact that he doesn’t seems to be enough. Genesis, by contrast, is a story where one God creates a world for His children to live in. He has no help, and there is no conflict. The only disobedience comes from God’s own children, but only because God gave them free will (and existence in the first place). It is unclear if the Ainur were given free will (or if they even have it at all), but even if they were they are certainly stronger figures than the men that God creates.
As a matter of fact, given the later passages of Ainulindale and The Silmarillion, it is questionable whether or not Illuvatar was meant to represent God at all. While he is the one creator, and He who bestows free will upon living things, he is remarkably absent. While the biblical God intervenes in the affairs of men and eventually sends his avatar in the form of his Son (I apologize for any misinterpreting, the Holy Trinity was always a bit fuzzy for me), Illuvatar is never mentioned after he promises that the Dwarves will have free will. Instead it is the Valar who create the world in preparation for humanity, the Valar who intervene in the affairs of men, and the King of the Valar, Manwe, who makes decisions about who should be allowed into Valinor, the closest thing to paradise that can be seen in The Silmarillion. Such a setup seems to bear more similarities to the Edda, where the father of all Giants has children who then become the Norse gods. There are obvious differences; the Giants live in opposition to the Gods, and the father of the Giants is killed. These are the themes that Tolkien discards in favor of more Christian ones. But the style and structure of creation remains the same: there is one creator, who spawns Gods, and is then absent until judgement day (some passages indicate that all Giants come back for Ragnarok).
Finally there is the trouble of validity. The Bible is, in some circles, absolutely canon. Genesis, to the most devoted, is the actual story of creation. Ainulindale doesn’t make this kind of claim. It is meant to be how the Elves perceived creation, but not necessarily the whole story (I imagine the Hobbits would have seen the events of creation a bit differently). This is further backed up in the other two framings of Ainulindale, where it is more of a myth, or a legend about how things happened. It is here that I am drawn to the work that seems to most resemble Ainulindale, Paradise Lost.
Milton takes a canonical creation story and adds depth. He adds characters who fight back against God, and action that takes place in Heaven, Hell, and Eden. Now Milton doesn’t claim to have “heard” this account from an angel, as the Elves do, but he does seem to employ the same methods Tolkien does. He has a set of themes that he wants to incorporate into his story, almost all of them Christian ones. He then writes a story that is inspired by the characters an existing framework, but is also an original story. I believe that Tolkien did a similar thing, but instead of using characters set up in the Biblical framework, he used his own. I don’t believe there is anything in the Legendarium that roughly equates to Genesis. Such a thing would detract from the power of Genesis itself, and Tolkien would be the last person to do that.