Why did "God" come down to earth/appear specifically to the Jews?

I will try to put together some passages from the early centuries Christian saints Gregory of Nyssa and(IV century) and Saint John Damascene (VIII century, an Arab saint who lived in the first century of Islam). You can see the respect with which they speak about God and about his incomprehensibility, but also you can say that God does not remain a distant unknown God:
We, therefore, both know and confess that God is without beginning, without end, eternal and everlasting, uncreate, unchangeable, invariable, simple, uncompound, incorporeal, invisible, impalpable, uncircumscribed, infinite, incognisable, indefinable, incomprehensible, good, just, maker of all things created, almighty, all-ruling, all-surveying, of all overseer, sovereign, judge; and that God is One, that is to say, one essences (Saint John)

The Deity cannot be expressed in words. And this is proved to us, not only by argument, but by the wisest and most ancient of the Hebrews, so far as they have given us reason for conjecture. For they appropriated certain characters to the honour of the Deity, and would not even allow the name of anything inferior to God to be written with the same letters as that of God, because to their minds it was improper that the Deity should even to that extent admit any of His creatures to a share with Himself. How then could they have admitted that the invisible and separate Nature can be explained by divisible words? For neither has any one yet breathed the whole air, nor has any mind entirely comprehended, or speech exhaustively contained the Being of God. But we sketch Him by His Attributes, and so obtain a certain faint and feeble and partial idea concerning Him, and our best Theologian is he who has, not indeed discovered the whole, for our present chain does not allow of our seeing the whole, but conceived of Him to a greater extent than another, and gathered in himself more of the Likeness or adumbration of the Truth, or whatever we may call it. (Or 30.17)

The language of blending would later be condemned at Chalcedon, on the prompting of the Antiochenes, for seeming to compromise the transcendence of the Son’s divine nature. In Gregory’s usage, however, it helpfully conveys both the narrative movement of the incarnation and also the mysterious union between God and humanity in Jesus: first there was the eternal Son of God, and then he took on the full reality of a human being, mixing it with himself to make one incarnate Lord. In Gregory’s view, the real danger lies not in compromising the integrity of these two realities, as the Antiochenes would argue, but rather in the opposite direction: the blending should not be misunderstood as being anything less than a real union. If our humanity is not fully united to God in Christ, then he is in fact two different sons and we have not been divinized in the incarnation. (p. 131) (Saint Gregory)

It would be maybe relevant in understanding that God could not show himself to his jewish club, that the jewish were prepared not for a Mesiah only for them. God tried to teach them exactly the contrary, the entire jewish history was a fight between God and his loved jews in order to prepare them for accepting to be open to God and to the others, their law tried to open them, not to make them a sect. Everything was an explosion in the history of Israel, and the prophets announced the day in which the law will be replaced by the communion in spirit.

of course the law tried to help them to avoid the things that their weakness could not bear, but the final purpose, the real purpose and meaning of the divine laws must be fulfilled, and it can not be fulfilled only trough running of your weakness and lack of power, the man was meant to become powerful and able to spread, to radiate his spiritual gifts to the others, not only to run of the waves of the evil without any interior power .

i mean the need to prepare the man must contain in itself the purpose, and the preparing in fact tries to put the roots of the love, faith, self sacrifice, joy, truth, life, holiness. People can't and don't want to understand totally what the meaning of God's act are, but, at their level, they sti8ll accept and somehow feel what they are doing, and so they can choose, as much as they can, to follow God's guidance. They can revolt and they might say after that actually what happen because of their weakness and lack of desire was what God told them to do, that this was the law and prophecies, but in that moment they are laying.

if you refer at the Trinity, this is another discussion. But you can see from the beginnings, the apostles message was incorrigible, but open to all, they were messengers (this is the meaning of the world "apostle") they were telling to all that now the world has changed, now the fight is possible, no everything returns to the Creator. They were living their lives exclusevely for the joy of telling to all and bringing all to their loved Christ, the savior of all and everything.

in this world of fight and choice, we are not yet free of the imperfection, we do not know anything. And even when we will, nothing will ever finish, God will always astonish us and joy us. We are not meant to leave the eternity in having the same pleasant spiritual or material joy, our joy can be real only when it will become the continuous share of something that will become continuously new. Our joy will never stop growing.

I will answe to this with the words of saint Gregory:
" But in as much as He strips Himself for us, in as much as He comes down (and speak of an exinanition, as it were, a laying aside and a diminution of His glory), He becomes by this comprehensible"
"And great multitudes followed Him, and He healed them there, where the multitude was greater. If He had abode upon His own eminence, if He had not condescended to infirmity, if He had remained what He was, keeping Himself unapproachable and incomprehensible, a few perhaps would have followed Him"

The great difficulty in trying to make a triumphalist model of Mesiah is that it does not have any chance to succeed without crashing the free will. God, who gave us the free will, will not make anything to force us to follow him, he does not even give a material proof of his existence. But how can God still do something for his creation? How can fight against the rebellion that he himself permits? He become man and suffered like us all the consequences of sin,all of them including death, desperation, all. And in this he showed his power, that he could not be defeated by death, that the laws, the body in he diluted himself could not keep his infinity bound. Without cheating, he defeated death and the consequences of the sin and because he become one of us (but without loosing or combining his divine nature what what is mortal) now we all can by believing in him and tryin to follow him to win through his victory and power the fight with the evil and sin.