We have numerous religious textual references, and ideas to backup the idea of who is the Messiah; yet as we see with Yeshua's fulfilment of prophecy, some people will go against it through a lack of study...
So is it ever really possible to actually prove it for sure using careful exegesis or are people to argumentative to really listen?
In my opinion.
Though those who believe Christ is the Messiah -and those who do not, yet believe in the Messiah -basically disagree that Christ is described in the following...
“And after the sixty-two weeks Messiah shall be cut off, but not for Himself;"
....all should be able to agree that the above does not describe something good happening to the Messiah -or, at the very least, does not describe some awesome and amazing show that he is the Messiah because he "wins" and everything is OK afterward. After Messiah is cut off, the following is described.... "And the people of the prince who is to come shall destroy the city and the sanctuary. The end of it
shall be with a flood, And till the end of the war desolations are determined."
Some do not believe Christ is the Messiah because he did not do the rest of the things the Messiah is described as doing -which WILL be an awesome and amazing show that he is the Messiah because he "wins" and everything is OK afterward.
When these things happen, it will be undeniable to all that the one is Messiah.
Neither believe he is finished fulfilling prophecy -but all should focus on righteousness regardless of present understanding.
Messiah will save and liberate "the Jews" regardless of whether a particular individual believes or understands -and "Jews" means the house of Judah FIRST (The house of Judah and the house of Israel were separated). Other prophecies refer to how the House of Israel (sometimes called the "lost ten tribes) will be reunited with Judah in the holy land.
"The LORD also shall save the tents of Judah first, that the glory of the house of David and the glory of the inhabitants of Jerusalem do not magnify
themselves against Judah."
The above does not specify Judah as opposed to the house of Israel, but those who inhabit the area around Jerusalem are primarily of the house of Judah -and that is specifically where Messiah will defend them against much of the world in no uncertain terms.
The following things precede the above quote -and have already been/are being fulfilled...... "Behold, I will make Jerusalem a cup of trembling unto all the people round about, when they shall be in the siege both against Judah
and against Jerusalem. And in that day will I make Jerusalem a burdensome stone for all people:
" "In that day will I make the governors of Judah like an hearth of fire among the wood, and like a torch of fire in a sheaf; and they shall devour all the people round about, on the right hand and on the left: and Jerusalem shall be inhabited again in her own place,
even in Jerusalem."
and this is next... essentially the whole world being gathered against Jerusalem (close neighbors first -followed by others). "all that burden themselves with it shall be cut in pieces, though all the people of the earth be gathered together against it. In that day, saith the LORD, I will smite every horse with astonishment, and his rider with madness: and I will open mine eyes upon the house of Judah, and will smite every horse of the people with blindness. And the governors of Judah shall say in their heart, The inhabitants of Jerusalem
shall be my strength in the LORD of hosts their God."
...and this is the very obvious way that Messiah will defend Jerusalem.... (think the one Moses saw the back parts of standing on the cloven mount of Olives)
"For I will gather all the nations to battle against Jerusalem;
The city shall be taken,
The houses rifled,
And the women ravished.
Half of the city shall go into captivity,
But the remnant of the people shall not be cut off from the city.
Then the Lord will go forth
And fight against those nations,
As He fights in the day of battle.
And in that day His feet will stand on the Mount of Olives,
Which faces Jerusalem on the east.
And the Mount of Olives shall be split in two,
From east to west,
Making a very large valley;
Half of the mountain shall move toward the north
And half of it toward the south.
Then you shall flee
through My mountain valley,
For the mountain valley shall reach to Azal.
Yes, you shall flee
As you fled from the earthquake
In the days of Uzziah king of Judah."
"And this shall be the plague wherewith the LORD will smite all the people that have fought against Jerusalem; Their flesh shall consume away while they stand upon their feet, and their eyes shall consume away in their holes, and their tongue shall consume away in their mouth. And it shall come to pass in that day,
that a great tumult from the LORD shall be among them; and they shall lay hold every one on the hand of his neighbour, and his hand shall rise up against the hand of his neighbour"
The point being that there will be no question who is Messiah at that point.
Those who are against "the Jews" might be offended by the above, but God will have allowed those in modern day Israel to be adversely affected partly because of their "turning of things upside down"... (God is equal -not a respecter of persons but of righteousness)....
"And the multitude of all the nations that fight against Ariel, even all that fight against her and her munition, and that distress her, shall be as a dream of a night vision"...................."so shall the multitude of all the nations be, that fight against mount Zion.
................"Surely your turning of things upside down shall be esteemed as the potter's clay: for shall the work say of him that made it, He made me not? or shall the thing framed say of him that framed it, He had no understanding"
.............."Is it not yet a very little while, and Lebanon shall be turned into a fruitful field, and the fruitful field shall be esteemed as a forest?"
Furthermore, there is one thing that happens on a human level -such as all of Israel inhibiting the area around Jerusalem -and another thing that happens on an eternal/immortal level.
Many of ALL NATIONS will already have been made immortal (described in more detail the New testament) -beginning to reign on Earth with the Lord/Messiah -even as the above is taking place.
Many focus on what will happen on the human level -and do not understand the eternal/immortal level. Humans will continue and repopulate the Earth -eventually to be made immortal also -and Israel will actually benefit and bless other nations as they do inhabit the area around Jerusalem
-but ALL NATIONS will already be represented among those already made immortal.
God is equal.
God will bless the houses of Judah and Israel in equal proportion -and more so -to his allowing them to be cursed and purified by extreme hardship -but it is actually God's intent to bless all peoples THROUGH and by all of Israel. That is why Israel was to be made a "peculiar nation" in the first place.
"And those from a strange land who join themselves to the Lord, to serve Him and to love His name, to be His servants, and keep the Day of Rest holy, and keep My agreement, even those I will bring to My holy mountain and give them joy in My house of prayer. Their burnt offerings and gifts will be received on My altar. For My house will be called a house of prayer for all people.” The Lord God Who gathers the people of Israel from other lands says, “I will gather yet others to them, besides those already gathered.”"