The solution will require thinking, compassion, and intellectual integrity. Simplistic sloganeering will not do it, and ignoring history would be fatal to the process.
There are those who seem to think, or at least say, that the Palestinian Arabs are more "indigenous", because there was a relatively large migration of Jews in the 20th Century.
And there are those who argue that the Jews are more "indigenous" because their presence extends back more than 1500 years prior to the conquest by the Arabs.
Both of these arguments are wrong, and neither is constructive.
The presence of the Jews in the Holy Land goes back more than 3000 years. In addition to the continuous residence of the Jews in the Holy Land throughout recorded history, the repeated genocides, enslavements, expulsions, and exiles to which they have been subjected prior to, and even after, the formation of the State of Israel, which thinned their numbers time and again, have never caused exiled or escaped diasporan Jews to forget their history, or to stop considering the Holy Land -- where the remains of their forefathers are buried -- as their sacred land. The land of Israel (Eretz Y'Isroel) and the city of Jerusalem (Y'Rushaloyim) are central to Jewish culture and religion in the Diaspora, and always have been. Almost every part of Jewish liturgy contains references to the Holy Land and to the Jews' being there and returning there. There are holidays which were celebrated in the middle ages in the cold steppes of Russia which were centered around fruits and growing seasons that existed only in The Holy Land. Synagogues in the Diaspora are constructed so that worshippers facing the ark, or cabinet, in which the Torah is kept, are facing in the direction of Jerusalem.
Some argue that the Palestinians are non-indigenous because there was no such thing as an "Arab" in the Holy Land until after the conquest by the Arabs in the 7th Century A.D. This is propaganda, not serious history, since (a) it is highly unlikely that the Palestinian Arabs of today are all purebred descendants of the Arabs from the Arabian Peninsula, (b) it is highly unlikely that all of the non-Jewish indigenous residents of the area in the 7th Century disappeared, moved, or became Jews; (c) there was no doubt intermarriage between the indigenous residents of that time and the Arabs from Arabia; and (d) many of those who identify themselves in that region today as Arabs, to the extent they are not relatively recent immigrants themselves, are no doubt the product of such intermarriage. And it would not be surprising to learn that many of them are in fact descended from Jews who opted to convert to Islam rather than be martyred by their Islamic conquerors.
It is likewise a myth that only the Jewish population's ranks have been swelled by immigration, while the "Arab" population has not. In fact, both the Jewish population and Arab population include vast numbers of relatively recent immigrants, who arrived during the past 100 to 150 years, and their descendants.
It is also a myth that all of the Jewish immigrants are from Europe, overlooking, e.g., the 3.5 million Jews in Israel who hail from the middle east. See, e.g., around a million who were forced out of other places in the Middle East by Islamic oppressors in the latter half of the 20th century alone. See, e.g. "Final Exodus of the Libyan Jews".
Another myth created recently has it that the Israelis who came from Europe aren't really "Jews" but are "converts" because of likely intermarriage in central Asia and in Europe. While a "racial purity" test is not an appropriate measure of who the Jewish people are, since they are not a race, but a people, the underlying factual premise is simply false. As the medical world and geneticists have known for decades -- the Jewish people have an unusually high level of genetic material in common with each other, despite their huge geographic dispersal.
To try to sort out who among the "Arab" population are indigenous and who are not, and who among the Jewish population are indigenous and who are not, or to try to determine which population is more indigenous than the other, is ludicrous, not constructive, and inhumane. It is a fact that both populations have long standing ties to the area, and that both populations have also been swelled by immigration.
More mythology is heaped upon us in suggesting that Israel "invaded" the occupied territories, ignoring the fact that each of the three major wars against Israel were initiated by the Arab world. On Israel's part, the 1948, 1967, and 1973 wars were purely defensive wars, not wars of "conquest". In 1948 the UN assigned Israel a tiny sliver of land, amidst a giant sea of Arab land, and gave it the right to share Jerusalem with its Arab neighbors. Unwilling to allow the Jews any right to even that small homeland in their ancestral home, the Arabs commenced a genocidal war intended to exterminate the Jews in the State of Israel. They immediately expelled the Jews from their ancestral home of Jerusalem -- which housed their most sacred site, and in which the Jews had resided for more than 3000 years, starting 1500 years before Islam was even invented (the Arabs who committed this "conquest" never termed their occupation of Jerusalem, which lasted from 1948 to 1967, an "occupation", or termed their mistreatment of Jews as "apartheid").
It is also propaganda to label Israel's Jewish nature as "apartheid", while ignoring Israeli law which bears no resemblance to apartheid, and ignoring the actual genocide, cultural genocide, pogroms, and other abuse of Jews by Arabs almost everywhere Jews have lived in the Arab world. If you want to see apartheid, study how Jews have been treated everywhere in the middle east except their home of Israel. (see note 1 below)
The Arabs lost their initial, 1948, war, and commenced several additional wars, which they lost as well. In each and every case the Arabs were the aggressor. With the first war, they gained territory, and with the second and third, they lost territory.
It is a fact that both peoples are "indigenous" and have longstanding ties to the land.
It is also plain that had the Arabs respected the right of the Jews to live in their ancestral homeland in peace there would have been no "occupation".
That is history. Now we have to look to the future.
If we are to move forward, each and every one of the living, breathing human beings who are born, live, and die in the region needs to be treated with dignity, respect, and compassion. Abuse of noncombatants, warring against civilians, abuse of prisoners, using civilians as human shields, war crimes, inhumanity to fellow man.... can have no place in the peace process.
Callous, politically motivated, warlike leadership is the last thing either side needs.
Inhumane behavior by the warring parties must stop, if peace is to be achieved.
1. Israel has a right to exist.
2. The Palestinian Arabs have a right to a state of their own.
3. War crimes, misconduct towards noncombatants, and other inhumanity must stop, and should be punished, or at least exposed through a 'truth and reconciliation" process.
4. Sloganeering, name calling, and rewriting history -- of the type that has been making the rounds on Twitter lately -- make the prospects for peace harder, not easier.
So I call upon all concerned to adopt a fair, balanced, honest, and humane approach to the problem of bringing peace to the Holy Land.
Note 1. Saudi Arabia's airline refuses to allow Jews to fly. This is apartheid.)