A very brief rundown, though I am not an expert, just a Jew who makes it some of my business to know some of this stuff, but TL;DR, both groups are about equally indigenous to the area, one's just also been diasporic for a long time:
Archeological evidence indicates the presence of a Kingdom of Israel (and later the divided kingdoms of Israel and Judah) at roughly the time that the Bible indicates the Davidic dynasty would have reigned. Contemporaneous with Judah would be Philistines, Idumeans, Nabateans, Samaritans (who are also Israelites, but not Jews, it's complicated) and various others.
The Nabateans, who were Arabs, even allied with the Jewish Hasmoneans (aka the Maccabees) in a war against the Seleucids. Jews were one people among many in the Palestine area. Like all kingdoms, there were border skirmishes, conquests, and warfare, but all of these groups were indigenous to the Levant. The Jewish Hasmoneans conquered a lot of Palestine, but they never had all of what's now considered Palestine, nor did they ever conquer Nabatea.
Then the Romans showed up, conquered the Hasmoneans, and created the Roman province of Judea, which covered most of northern Palestine, while the Nabatean Kingdom allied themselves with the Romans and remained an independent client state a while longer (they would become the Roman province of Arabia Petraea when Emperor Trajan got hungry for more territory).
The Judeans did not take kindly to being conquered (and a certain first-century guy got crucified in this time, among several others), and launched the Bar Kochba rebellion. In response, the Romans did a genocide, flattened Jerusalem, kicked out all the Jews (the start of the Jewish Diaspora), and renamed the province to Syria Palestina. The region had already been called Palestine for a long time prior, but now it was the official Roman name of the province. The ban on Jews was not strictly enforced, and Jews did gradually come back to the region, but the dynastic power the Hasmoneans once held was broken for good, and most Jews were scattered across the Roman Empire, the Persian Empire, and Arabia.
The region traded hands between the Romans, the Byzantines, the Sassanids, and others. The Nabateans did relatively well for themselves, as did the other inhabitants of the region. At one point the Ghassanids, who were Christian Arabs, created two client kingdoms in Palestine that served as a buffer zone between the Christian Byzantines and their pagan Persian and Lakhmid rivals. The Samaritans revolted at one point, and were brutally put down by the Byzantines. In 613, the Sassanid Persians invaded Palestine, and the Jewish population rebelled against the Byzantines, hoping to reestablish Judea. They failed miserably.
Less than two decades later, Palestine was conquered by the Rashidun Caliphate, and its population was thoroughly Arabized. The same people were living there, but they now spoke Arabic and were by-and-large Muslim, though Christians and Jews still lived there. Palestine remained under various caliphates up until the Crusades, where it was briefly under the control of Europe, after which Saladin replaced the caliphates with the Ayyubid Sultanate. The Ayyubids were eventually overtaken by the Mamluks, who fought off the Mongols, until the Ottoman Turks conquered Palestine in the 1400s.
Palestine remained a province of the Ottoman Empire right up until the early 20th century, when increasing Turkification efforts and the arrival of Jewish Zionists who wanted to essentially reconstitute Judea (Zionism is complicated) led the Arab population to form a distinct Palestinian identity and vie for independence. This nationalism continued through World War One, when Britain and France colonized the region and divided it up into modern-day Syria, Lebanon, Jordan, and Palestine - the British Mandate of Palestine had agreed to "give" the land they colonized to both the Zionists and the Palestinians, playing the two groups against each other. The Palestinians staged a revolt against the British and the Zionists in 1936, which failed, and then the Zionists kicked out the British and established the State of Israel in 1948.
So ultimately, both groups are indigenous to the region, but the Zionists acted as colonizers and committed acts of ethnic cleansing to establish Israel. Sorry this was long, hope it was informative.