Y'shayahu / Isaiah 9:5 - 6 (6:7 in Christian bibles) says nothing a "son given deity (god)" status. This is a concept totally foreign and rejected in the T'nach which tells us time and time and time again that there is only One G-d -- and He is not a human being.
There are 11 supposed prophecies tied to this one passage by the list maker, but in a nutshell the Christians state that the passage reads: “And His name will be called Wonderful Counselor, Mighty God, Eternal Father, Prince of Peace.” and that all those superlatives are speaking about Jesus. . . after all what other child could be called "mighty G-d" or "everlasting Father"? Thus they conclude that this must be about Jesus who was "god" on earth.
This is distorting the passage.
In fact this passage is stating that G-d Himself is naming and blessing a child by calling that child a prince of peace.
Properly translated it is not His name (notice the capital "H"? There are no capital letters in Hebrew, that capital "H" is to infer god) qualities to the child will be called. . . and all those titles follow. . .
But that is not how the passage actually reads. It should be translated as "the wondrous adviser, the mighty G-d, the everlasting Father, called his name, "the prince of peace."
Let's parse this.
So the child is not G-d.
The child is not the wondrous adviser, the mighty G-d or the everlasting Father. Those are titles for G-d Himself.
G-d names the child a prince of peace.
A mistranslation has caused Christians to read the passage as if the child is being called "wondrous adviser, mighty G-d" and so on -- but that is not the meaning of the passage.
All of this is in the past. Christian translations may put it in "future" tense ("for unto us a child is born"), but it is actually in past tense. "For a child has been born to us." יֻלַּד־ / yulad "was sired" is in the perfect / past tense. The child spoken of in this passage has already been born, not predicting that some 700+ years in the future Jesus will be born and be a deity.
נִתַּן־לָ֔נוּ / n'tan lanu "was given to us."
וַתְּהִי - "and has-been" (past tense) The future tense in this case, including the preposition "and", 'וְ', would be וְהָיְתָה (e.g., Yoel / Joel 4:17) - also different.
Y'shayahu / Isaiah 9:5 - 6 is speaking about the birth of חִזְקִיָּ֫הוּ / Hizkiyyahu / Hezekiah), the son of King Ahaz (of Y'shayahu / Isaiah 7 fame). At the time of Y'shayahu / Isaiah 9:5 - 6 the child already was born (past tense) so it could not possibly be about Jesus who would not be born for 700+ years. The image is of the seal of חִזְקִיָּ֫הוּ / Hizkiyyahu / Hezekiah which was discovered along 33 other seals, figurines and ceramics, inside a collapsed building adjacent to Temple Mount in Jerusalem. The seal reads “Belonging to Hizkiyyahu / Hezekiah son of Ahaz, king of Judah” and features a symbol of a two-winged sun disk with ankh symbols on either side.
There is nothing in this passage that even suggests that the son (who has already been born 700+ years before Jesus) is in any way divine, let alone a deity.
The child in question is called a "peace prince."
Jesus was not a prince (he was supposedly an itinerant preacher, son of a carpenter).
Jesus did not live in a time of peace -- the Romans were cruel rulers and there were constant fights, tens of thousands of crucifixions of Jews by the Romans and eventually an open war where Jerusalem was destroyed, and eventually the Jews were exiled.
No, the term "peace prince" (prince of peace) does not fit Jesus.
But it does fit חִזְקִיָּ֫הוּ / Hizkiyyahu / Hezekiah. This is one of the 11 claimed "prophecies" on the list so not much time will be spent here to address it -- but the death knell to the specific claim that a son will be given deity is totally false. Nowhere in Isaiah (or the rest of the T'nach) does it say that any human will ever be a "son of G-d" let alone a deity.
Pagan, not biblical.
There is no support in the T'nach for the Christian doctrine that Jesus was G-d's "begotten" son, i.e., that he was fathered by G-d through an act of procreation*, as claimed in the Christian bible. Indeed, the T'nach teaches that we are all G-d's sons and daughters and that "My (G-d's) firstborn son is Israel." (Sh'mot / Exodus 4:22).
In D'varim / Deuteronomy 14:1 G-d tells us "You are children of the L-rd, your G-d."
Hoshea / Hoseah 2:1 tells us that the Jews are "children of the living G-d", and Hoshea / Hosea 11:1 states "For, when Israel was young, I loved him, and from Egypt I called My son."
Individuals in the T'nach are also called G-d's son. In T'hillim / Psalm 2:7 Dovid HaMelech (King David) is told "You are My son; this day have I begotten you." Shlomo HaMelech (King Solomon) is also called G-d's son in Shmuel Beit / 2 Samuel 7:14 and Divrei Hayamim Alef / 1 Chronicles 22:9 - 10.
However, none of the sons of G-d (the Jewish people or individuals such as David and Solomon) are the biological son of G-d (a very pagan idea). All of us have human parents, but all of us are also His children. Being G-d's son or daughter does not make any of us a deity, G-d forbid. The idea of a divine humna is unbiblcal, and the bible tells us clearly:
"I am the first and I am the last and besides Me there is no other.” (Yeshayahu / Isaiah 44:6).
“Hear (Listen) O Israel, The L-rd our G-d, the L-rd is One.” (D’varim / Deuteronomy 6:4).
“That you will know that G-d, He (ה֣וּא – singular) is the (singular) Supreme Being and there is none besides Him." (singular) D'varim / Deuteronomy 4:35.
"Now, O L-rd our G-d, deliver us from his hand, so that all kingdoms on earth may know that You ALONE, O L-rd, are G-d.” (T'hillim / Psalm 113:5).
"Before Me (SINGULAR) no god was formed, nor will there be one after Me (SINGULAR). I (SINGULAR), even I (SINGULAR), am the L-rd, and besides Me (SINGULAR) there is no savior.” (Yeshayahu / Isaiah 43:11).
"So said the L-rd, your Redeemer, the ONE who formed you from the womb, “I am the Lord Who makes everything, Who stretched forth the heavens alone, Who spread out the earth ALONE (לְבַדִּ֔י).” (Yeshayahu / Isaiah 44:24).
"I am the L-rd, and there is no other; besides Me there is no G-d… I will strengthen you…I order that they know from the shining of the sun and from the west that there is no one besides Me; I am the L-rd and there is no other!” (Yeshayahu / Isaiah 45:5-6).
One reason that Y'shayahu / Isaiah 9:5 - 6 (6:7 in Christian bibles) is such an oft referenced "proof" text is the very thought that it somehow proves that Jesus is G-d Himself. The passage says no such thing and yet again we are faced with a distortion of the passage, complicated by mistranslation (purposefully?) to aid in this misleading thought.