If some man came and claimed to be God, what proofs could you establish from scripture/text that this would not be possible?
Two explicit verses come to mind:
לא איש אל ויכזב -- "God is not a man that he would lie"
כי לא אדם הוא להנחם -- "For he is not a man that he would change is mind"
1 Samuel 15:29
(My somewhat loose translations)
Bilam juxtaposes God and man in Num 23:19:
לֹא אִישׁ אֵל וִיכַזֵּב, וּבֶן-אָדָם וְיִתְנֶחָם; הַהוּא אָמַר וְלֹא יַעֲשֶׂה, וְדִבֶּר וְלֹא יְקִימֶנָּה.
God is not a man, that He should lie; neither the son of man, that He should repent: when He hath said, will He not do it? or when He hath spoken, will He not make it good?
Moses says in Deut 4:12 and 15 that no image was seen at the revelation at sinai, which precludes any image, including man:
וַיְדַבֵּר יְהוָה אֲלֵיכֶם, מִתּוֹךְ הָאֵשׁ: קוֹל דְּבָרִים אַתֶּם שֹׁמְעִים, וּתְמוּנָה אֵינְכֶם רֹאִים זוּלָתִי קוֹל.
And the LORD spoke unto you out of the midst of the fire; ye heard the voice of words, but ye saw no form; only a voice.
וְנִשְׁמַרְתֶּם מְאֹד, לְנַפְשֹׁתֵיכֶם: כִּי לֹא רְאִיתֶם, כָּל-תְּמוּנָה, בְּיוֹם דִּבֶּר יְהוָה אֲלֵיכֶם בְּחֹרֵב, מִתּוֹךְ הָאֵשׁ.
Take ye therefore good heed unto yourselves--for ye saw no manner of form on the day that the LORD spoke unto you in Horeb out of the midst of the fire--
Ezekiel, in what is probably the most explicit recorded depiction of God's 'image' in Tanach, Ezek 1:26, says he saw an image as the appearance of a man, as opposed to his describing the image of a throne, with no preposition. in 1:28, Ezekiel describes what he saw as 'the glory of God', not God Himself:
וּמִמַּעַל, לָרָקִיעַ אֲשֶׁר עַל-רֹאשָׁם, כְּמַרְאֵה אֶבֶן-סַפִּיר, דְּמוּת כִּסֵּא; וְעַל, דְּמוּת הַכִּסֵּא, דְּמוּת כְּמַרְאֵה אָדָם עָלָיו, מִלְמָעְלָה.
And above the firmament that was over their heads was the likeness of a throne, as the appearance of a sapphire stone; and upon the likeness of the throne was a likeness as the appearance of a man upon it above.
כְּמַרְאֵה הַקֶּשֶׁת אֲשֶׁר יִהְיֶה בֶעָנָן בְּיוֹם הַגֶּשֶׁם, כֵּן מַרְאֵה הַנֹּגַהּ סָבִיב--הוּא, מַרְאֵה דְּמוּת כְּבוֹד-יְהוָה; וָאֶרְאֶה וָאֶפֹּל עַל-פָּנַי, וָאֶשְׁמַע קוֹל מְדַבֵּר.
As the appearance of the bow that is in the cloud in the day of rain, so was the appearance of the brightness round about. This was the appearance of the likeness of the glory of the LORD. And when I saw it, I fell upon my face, and I heard a voice of one that spoke.
Rambam in his introduction to Chelek cites the verse (Yeshaya 40:25) ואל מי תדמיוני ואשוה, to whom can you compare Me that I would be equatable? He explains: If Hashem had a body, He would be equatable to other creations that have bodies.