I think first use of Jew/Yehudi to mean Hebrew instead of just a Tribe is in Jeremiah 34.
I'm wondering if at first Judaei and Ioudaioi would have had a geographical sense, all inhabitants of Judaea, and only later been restricted to adherents of the Jewish faith? In early Christian writings it's clearly a religious label, but I'm wondering if pagan Romans would have been careful in how they used the term. Of course there were Jews in Rome and in various provinces of the Roman Empire even before the destruction of Jerusalem. Tacitus in Histories Book 5 seems to use Judaei as a religious/ethnic term in his unfriendly and laughably ignorant discussion of the Jews. That was written a good deal after the destruction of Jerusalem.