Seventy weeks are decreed for your people and your holy city to stop their transgression, to put an end to sin, to make atonement for iniquity, to bring in everlasting righteousness, to seal up vision and prophecy, and to anoint the Most Holy Place. (Daniel 9:24 BSB)
They will fall by the edge of the sword and be led captive into all the nations. And Jerusalem will be trodden down by the Gentiles, until the times of the Gentiles are fulfilled. (Luke 21:24 BSB)
I do not want you to be ignorant of this mystery, brothers, so that you will not be conceited: A hardening in part has come to Israel, until the full number of the Gentiles has come in. (Romans 11:25 BSB)
Many philosophies and religions (Buddhism, Zoroastrianism, Jainism, Confucianism, Taoism, Platonism) come to birth around the year 500 BC. Socrates, Buddha and Confucius all lived at around that time. Has anyone wondered why is the period around 600 BC to 500 BC the age for sprouting philosophies and religions?
On 14th August 586 B.C. king Nebuchadnezzar of Babylon razed and burned the Temple of God in Jerusalem. The Glory of God had departed from the Temple some time before that happened (Ezekiel 10). Historians will not tell you this, but from that day onward, Jerusalem was trampled under the feet of the Gentiles and the times of Gentiles began.
According to some historians, this is the beginning of the second wave civilisations which lasted from 600/500 BC to 500/600 AD. The Islamic calendar began in 622 AD.
There were four civilisations at the beginning of this period, the Greek, Persian, Indian and Chinese civilisations. These four civilisations will persist in various forms until about seven years before the end of the times of the Gentiles. Then the ten toes kingdom from the Roman empire will conquer the other three civilisation to start a world government under the anti-Christ.
As for the Gentile powers ruling Jerusalem while the Jews are living there are represented by the statue in king Nebuchadnezzar's dream (Daniel 2:31-45) and also the four beasts (Daniel 7:1-28) in Daniel's dream. These would be Babylon, Persia, Greece and Rome. The Gentile powers that ruled Jerusalem when the Jew were not staying there were not listed in the dreams. They are the Arabs, Crusaders, Mamelukes, Ottoman and finally the British. Here is the full list of Gentile invaders from the beginning - Egyptians, Assyrians, Babylonians, Persians, Greek, Romans, Byzantines, Arabs, Crusaders, Mamelukes, Ottoman, British.