You do know that anyone can and has filled that role in the past...example is Cyrus, who was an "annointed one"
"the" messiah is one specific anointed one.
John 12:12 On the next day much people that were come to the feast, when they heard that Jesus was coming to Jerusalem,
13 Took branches of palm trees, and went forth to meet him, and cried, Hosanna:
Blessed is the King of Israel that cometh in the name of the Lord.
14 And Jesus, when he had found a young ass, sat thereon; as it is written,
15 Fear not, daughter of Sion:
behold, thy King cometh, sitting on an ass's colt.
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Mark 15:31 Likewise also the chief priests mocking said among themselves with the scribes, He saved others; himself he cannot save.
32 Let
Christ the King of Israel descend now from the cross, that we may see and believe. And they that were crucified with him reviled him.
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John 19:19 And Pilate wrote a title, and put
it on the cross. And the writing was, JESUS OF NAZARETH
THE KING OF THE JEWS.
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A little background as why I don't disagree with you that Cyrus an annointed one could be considered "a messiah". (But not "the" messiah).
Back in 2004, I joined the Messiah Truth discussion board, which is a Jewish (Judaism) site intended to be a counter missionary site, against Jews converting to other religions other than Judaism.
I have 1,000's of exchanges there, arguing with them, and being educated by what they believe in the process. It you go there, for the best results, just ask questions on what they believe.
Anyway, Sophiee and Uri there made the point that there were "countless" messiahs, as the kings and priests of Israel are considered anointeds. Including some from other nations like Cyrus, as you have noted, and is also in the text of the bible.
But "the" messiah is different as one specific "King of Israel", descended from David, to lead Israel and the world into the messianic age - which includes peace and safety.
The requirements of the messiah, as the Jews are looking for, going by their theologian the RAMBAM, includes that the messiah will fight the battles of God in defending Israel. They gave a bible basis for that belief.
Which, having that gained knowledge, and from the text of the bible, the little horn from in Daniel 8:23 who "stands up" (an idiom for prepares to go to war), heading south and east toward Israel waxing strong in Daniel 8:9, could appear to the Jews as the messiah. If he does so with the intent of opposing the Gog/Magog invaders.
From Ezekiel 38-39, a condensed form of the end times events is Gog/Magog, then the seven years, then Armageddon and Jesus's return.
So coupling those things together, it appears that the prince who shall come in Daniel 9:26-27, is the little horn person, coming from Europe in the wake of Gog/Maog's destruction, in a transitional role to becoming the Antichrist - will be perceived as the messiah by the Jews.
"Anti" instead of and against - the rightful King of Israel - Jesus - the Christ. The another, Jesus said the Jews would accept coming in his own name.
To become the King of Israel (but as the Antichrist, one that God does not approve of - coming in his own name), the person has to be anointed by a known prophet - according to the Jews. Historically, Saul and David by Samuel the prophet. Solomon by Nathan. They are expecting Elijah.
And it so happens in Revelation that there is such a prophet who mimic's what Elijah did as far as calling fire down from heaven.
So it appears to me that the false prophet, claiming to be Elijah, will anoint the prince who shall come as the King of Israel messiah. It is at that point the person becomes the Antichrist, and is in that role until he later betrays the Jews by claiming to have achieved God-hood. Ending his time as the Antichrist, King of Israel.
For the remainder of the 7 years, he will be the beast, a role of being the King of the Roman Empire of the end times.
He starts out as the little horn - as the King of the Roman Empire of the end times - he is king #7 of Revelation 17:10. Then, after a stint as the Antichrist, King of Israel, he becomes king 8 of Revelation 17:11, the beast King of the Roman Empire of the end times.
Which the ten kings of the fourth empire (in Daniel 7) give their Kingdom (the EU) over to him. Revelation 17:17.
So what to watch for on the near term horizon is the EU reorganizing to a ten leader form of government with one king over them (the little horn). The person should be a Jew and his religion Judaism (he will likely be into Kabballah, as the occult source of his rise to power).
I should note that it all ends well for the Jews and Israel in the end. But it will be tough go along the way.