Jordanians. And they were just generic "Arabs" prior to the establishment of Jordan. Prior to that they were just citizens of the Ottoman Empire, part of the Syrian province. Just one of the many peoples in the region who spoke Arabic, not significantly different from any of the others in the surrounding areas.
It's interesting that you start with the 7th century. For if you start earlier the inhabitants of the area would be by far mostly Christians and Jews.
I started in the 7th century because that's when it was conquered culturally by the Muslims. But the local inhabitants were not racially purged (do you have any idea how logistically imposable it would have been for the Arabs to kill every individual in Roman Palestine?). Most simply converted, or left. It is the descendants of the local people who converted to Islam over a period of several centuries prier to the Crusades (though even then, as now, there were many pockets of Christian minorities, the oppression of whom was one of the main causes of the Crusades) who are what we call Palestinians. They are not genetically pure Arabs, they are a mix of Arab conquerors and the original inhabitants just as the modern French are not pure genetic Franks, mostly they are still Gauls. Your misunderstanding of the nature of the problem stems from your mistaken assumption that culture is equatable with genetic ethnicity. The Palestinians may be cultural Arabs because they are Muslim and speak Arabic, but that doesn't make them genetically Arab. This is what I mean by the genetic problem, since if we establish a Jewish right to the region on historical grounds we have to deal with the problem that not all the Jews left, some converted to Islam (Some to Christianity first and then Islam, and some vis versa probably).
Now remember I'm not saying definitively that the Palestinians have a right to sovereignty. I'm just trying to find a good reason for them to stop attacking Israel. I don't buy the argument that they don't exist and there for should accept Israel. It's utterly pointless to say the indigenous inhabitants of the region we call Palestine don't exist.
But I don't see any kind of logical solution to the problem, least not a solution which doesn't cancel both the Israelis right to a state as well as the Palestinians.
Barring the rise of a Palestinian Gandhi I don't think there is a solution. But even then a Palestinian Gandhi would probably be politically bad for Israel. Ironically the fact that the Palestinians use the violent tactics that they do probably is one of the reasons Israel has the support it does since no sane moral person would support the terrorist.
And so I come back to Israel needing to establish complete military hegemony in the whole region. The Muslims can afford to play the dithering game on the issue of Israeli right to existence. They don't have to attack Israel openly anymore, it's more effective for them to finance domestic terrorism against Israel. But we know that a great majority of Muslims want to see Israel gone. And, with the Might makes Right philosophy on which, as you say, Israel is justified, I can see no reason why they should stop. Which means Israel must crush her neighbors militarily so that she can assure her long term survival. But since that's not an option I don't know what will make it work.
I don't like philosophical loose ends, and the reasoning for Israels existence as established by the idea that they are stronger, or that they ethnically have more of a right then the locals leaves too many philosophical loose ends. Not to mention that the latter tends to rely on the former for practical enactment.
Personally my sympathy is with the Israelis, because I cannot condone terrorism and further I'm prejudiced against the Muslim religion. But personal sympathy and prejudice don't make rational arguments.