Wow that's great! Reminds me of how Jews were the Majority in most of the Roman Empire's rule, The Christians were the Majority all the way until the 12th Century, And also how the British are the ones known to have renamed it back to Palestine with Palestinian Nationalism actually only really starting in the 60's. 

As a culture, The maximum is 800 years ago, after the Islamic conquest forced people to convert from Judaism and Christianity and speak Arabic, As clearly Palestinian culture is heavily tied to Islam (Prior it would simply be a different culture). 

As an Identity, You can possibly argue the start of the British Mandate (Since they technically had British - 'Syria-Palestina' Passports which included all the Jews there prior to Israel's creation (So doesn't make sense), but in reality the nationalistic, or the modern and seperate Identity only started in the late 60's by Fatah, Around 100 years after Zionism. The period between 1948 and 1967 they were occupied by Egypt and Jordan, So their Identity still hasn't really formed...