"And I shall put enmity between you and the woman and between your seed and her seed. He will bruise you in the head and you will bruise him in the heel." — Gen 3:15

"Why the reverse order as far as the resolution of the enmity?" @Timothy Kline

Why does the text mention that the bruising of the head to the serpent occurs before the bruising of the heel of the woman's seed if the heel wound brings about the serpent's destruction?

This appears to be a matter of prophecy. The head bruising/deathstroke was Babel.

"You said in your heart, 'I will ascend to heaven; above the stars of God I will set my throne on high; I will sit on the mount of assembly in the far reaches of the north." Ish 14:13

"Come, let us go down and there confuse their language, so that they may not understand one another's speech." So the LORD dispersed them from there over the face of all the earth, and they left off building the city. Therefore its name was called Babel, because there the LORD confused the language of all the earth. And from there the LORD dispersed them over the face of all the earth." Gen 11:7-9

"I saw in the visions of my head as I lay in bed, and behold, a watcher, a holy one, came down from heaven. He proclaimed aloud and said thus: 'Chop down the tree and lop off its branches, strip off its leaves and scatter its fruit. Let the beasts flee from under it and the birds from its branches." Dan 4:13,14

"And the beast that I saw was like a leopard; its feet were like a bear's, and its mouth was like a lion's mouth. And to it the dragon gave his power and his throne and great authority. One of its heads seemed to have a mortal wound, but its mortal wound was healed, and the whole earth marveled as they followed the beast." Rev 13:2

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The prophetic wound to the serpent's ego came at Babel when that boastful ideology was birthed at the Tower and spread prophetically to Nebbi and finally to the Little Horn and Wild Beast.

The head wound to the serpent's boastful ideology is healed in the form of the lion's mouth of Rev 13 and the healed condition of the lion in Dan 7 from that of Nebbi in Dan 4.

Dan 4:33 "His hair grew long just like eagles feathers and his nails were like birds claws."

Dan 7:4 "The first one was like a lion, and it had the wings of an eagle. I watched until its wings were plucked out,

Dan 4:24 "Your dwelling will be with the beasts of the field," and it was lifted up from the earth and was made to stand up on two feet like a man."

Dan 4:6 "Let its heart be changed from that of a human, and let it be given the heart of a beast," and it was given the heart of a man."

"And its mouth was like a lion's mouth." Rev 13:2

"It opened its mouth to utter blasphemies against God, blaspheming his name and his dwelling." Rev 13:6

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In the text, serpents bite the enemy's heels to falter their trailing entities.

"Dan shall judge his people, As one of the tribes of Israel. "Dan shall be a serpent in the way, A horned snake in the path, That bites the horse's heels, So that his rider falls backward." Gen 49:16,17

"As for Gad, raiders shall raid him, But he will raid at their heels." Gen 49:19

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As the remaining of Christ's brothers are attacked just prior to our Lord's appearance in the clouds, the world imagines this act will separate His interests and this planet from their desire to remain. How God will laugh as their destruction swiftly commences.

"He had a little scroll open in his hand. And he set his right foot on the sea, and his left foot on the land." Rev 10:2

"Let us burst their bonds apart and cast away their cords from us.” He who sits in the heavens laughs;
the Lord holds them in derision. Then he will speak to them in his wrath, and terrify them in his fury, saying, “As for me, I have set my King on Zion, my holy hill.” Psm 2:3

"For thus said the LORD of hosts, after his glory sent meb to the nations who plundered you, for he who touches you touches the apple of his eye: “Behold, I will shake my hand over them, and they shall become plunder for those who served them. Then you will know that the LORD of hosts has sent me." Zech 2:8,9

"And he shall pitch his palatial tents between the sea and the glorious holy mountain. Yet he shall come to his end, with none to help him." Dan 11:45

Joshua