My source for 'Athens' or Athene as a Pre-Greek word is from:
Beekes, Robert S., Etymologicval Dictionary of Greek, 2009
Whether the word was applied to the Goddess or the settlement first is, at least as of several years ago, still hotly debated.
The (archeological) evidence of the first Greek speaking inhabitants dates back to before 1400 BCE. By that date, there was a Mycenean fortress on the Acropolis, for which there is still evidence of cylopean walls. But there is additional archeological evidence of habitation going back to 3000 BCE. Unfortunately, I don't know of any evidence as to what language or language family these people may have spoken - they appear to have been pre-literate.
Note that there is little or no evidence e for the kind of destruction in Athens around 1200 BCE that hit Mycenae and Pylos and other major Mycenean centers, and Athenians themselves in the classical era always claimed that they were 'pure Ionian' and the Dorian invasions never touched them. The lack of any trading partners and general collapse of political authority after the 12th century BCE still meant Athens was an economic backwater for at least 150 - 200 years.
The 'rise' of Athens is indeed usually dated at Solon, but note that Solon's reforms were required because Athens already had been a major center of trade for 2-300 years or so and the economic disruption caused by the conflict between 'traditional' wealth from land and wealth from trade was threatening to start a civil war in the polis.
This, at least, is what I was taught in University classes in the late 1960s which covered 'Cleisthenian Democracy in Athens' and 'The Polis in classical Greece'. I confess I have not kept up with current archeological and historical details on the subject once I left school.