Is there archaeological evidence for “the Tower of Babel” (Gen 11:4)?

There is some archaeological evidence for a very early ziggurat on what is believed to be the original site of Babylon. A few years ago, a tablet was found that purports to be a picture of a ziggurat at Babylon., although this one was a reconstructed tower built a the behest of Nebuchadnezzar (who lived 2,000 years later). And Titus Kennedy, in Unearthing the Bible, also points to the story of Enmerkar (a name that shares important consonants with “Nimrod”), which shares interesting parallels to the Biblical Babel story, with significant differences. In that regard the epic bears rough likenesses that are themselves roughly similar to likenesses that other Mesopotamian and Egyptian texts have with other Gen 1-11 stories, such as about the creation, Eden, and Noah. As with those stories (see above), the question is whether the Bible story, or its folk ancestor narratives, are the origin of the other narratives, or vice-versa—or if all the stories share a common ancestor. I am inclined to think the latter is the case.