This is a good article that covers the ancient evidence and brings the current scholarly debate up to date.
In sum, no archaeological excavation has recovered on evidence for those Hanging Gardens at the site of Babylon. Where does that leave us?
One possibility is that they are entirely legendary. Another is that later Greek authors (who produced what I call the Greek Fantasy Babylon tradition) accidentally misplaced hanging gardens of the Assyrian capital, Nineveh, to Babylon. But at least one Assyriologist thinks they could have been terranced along the huge walls of Babylon. Presumably that means that traces of them might not survive today.
The article asserts that the existence of the legendary Assyrian Queen Semiramis is debated, but I'm not sure what this means. There was an historical Assyrian Queen Shammuramat (cf. here) who ruled in the late eighth century BCE. She was clearly the inspiration for the legendary Queen Semiramis, whose apocryphal exploits included the founding of Babylon. No one doubts her existence or that she didn't found Babylon (which existed for many centuries before her).
Background here and links.
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