So has YHWH always had a genome?

Depends how you look at it. It was only really a physical matter during The Incarnation and Christophanies itself, and the way we look at the genome itself. However, God always intended for The Incarnation to happen, thus such a genome would have been pre ordained.

Isaiah 52:13-53 is referring to Jesus

Isaiah 52:13-53:12:

Behold, my servant shall act wisely; he shall be high and lifted up, and shall be exalted. As many were astonished at you— his appearance was so marred, beyond human semblance, and his form beyond that of the children of mankind— so shall he sprinkle many nations. Kings shall shut their mouths because of him, for that which has not been told them they see, and that which they have not heard they understand. Who has believed what he has heard from us? And to whom has the arm of the LORD been revealed? For he grew up before him like a young plant, and like a root out of dry ground; he had no form or majesty that we should look at him, and no beauty that we should desire him. He was despised and rejected by men, a man of sorrows and acquainted with grief; and as one from whom men hide their faces he was despised, and we esteemed him not. Surely he has borne our griefs and carried our sorrows; yet we esteemed him stricken, smitten by God, and afflicted. But he was pierced for our transgressions; he was crushed for our iniquities; upon him was the chastisement that brought us peace, and with his wounds we are healed. All we like sheep have gone astray; we have turned—everyone—to his own way; and the LORD has laid on him the iniquity of us all. He was oppressed, and he was afflicted, yet he opened not his mouth; like a lamb that is led to the slaughter, and like a sheep that before its shearers is silent, so he opened not his mouth. By oppression and judgement he was taken away; and as for his generation, who considered that he was cut off out of the land of the living, stricken for the transgression of my people? And they made his grave with the wicked and with a rich man in his death, althoughhe had done no violence, and there was no deceit in his mouth. Yet it was the will of the LORD to crush him; he has put him to grief; when his soul makes an offering for guilt, he shall see his offspring; he shall prolong his days; the will of the LORD shall prosper in his hand. Out of the anguish of his soul he shall see and be satisfied; by his knowledge shall the righteous one, my servant, make many to be accounted righteous, and he shall bear their iniquities. Therefore I will divide him a portion with the many, and he shall divide the spoil with the strong, because he poured out his soul to death and was numbered with the transgressors; yet he bore the sin of many, and makes intercession for the transgressors.