What is the origin of livestock sacrifice for Eid ul-Adha?

Question

I was just reading about livestock sacrifice during Eid ul-Adha, prompted by seeing it on Muslim charity sites, such as Muslim Aid Australia.

Affluent Muslims who can afford it sacrifice their best halal domestic animals (usually a cow, but can also be a camel, goat, sheep, or ram depending on the region) as a symbol of Abraham's willingness to sacrifice his only son. The sacrificed animals, called aḍḥiya (Arabic: أضحية‎‎), known also by the Perso-Arabic term qurbāni, have to meet certain age and quality standards or else the animal is considered an unacceptable sacrifice. -- Eid al-Adha, Wikipedia

Qurbāni is the sacrifice of a livestock animal during Eid al-Adha. -- Qurbani, Wikipedia

I hear it's symbolic of Prophet Abraham's sacrifice of his son (Qur'an 37:100-112). I've seen several conflicting claims about what happens next (God gave him a sheep to sacrifice instead; God substituted a ram in Ismail's place; either the knife is turned over in his hand or copper appears on Ishmael), but the Qur'an says:

And when they had both submitted and he put him down upon his forehead, We called to him, "O Abraham, You have fulfilled the vision." Indeed, We thus reward the doers of good. -- Qur'an 37:103-105

And I don't see mention of an animal (or anything) being killed.

Every year, thousands of animals are sacrificed by Muslims. It is, in a sense, a symbolic expression that a Muslim can sacrifice anything he has in order to worship Allah, comply with His command and give up anything he has for His sake. -- Questions on Islam

I'm a vegetarian, so I'm hesistant to play a role in killing an animal. Moreover, the Qur'an says they had both submitted (Abraham and his son), whereas an animal cannot agree to its own sacrifice. (It seems I'm not the only one uncomfortable with this: see Giving money instead of buying an animal and Celebration of Eid ul Adha for a vegan muslim). So I'm trying to figure out where the idea of livestock sacrifice came from.

Question: What is the origin of livestock sacrifice for Eid ul-Adha?

Answer 1

All Praise to Allah Subhanahu wa Taala and blessings of him be on Prophet Muhammad peace be upon him his family and companions

Just providing some references to simplify.

Narrated Jabir ibn Abdullah:

The Prophet (ﷺ) sacrificed two horned rams which were white with black markings and had been castrated. When he made them face the qiblah, he said: I have turned my face towards Him. Who created the heavens and the earth, following Abraham's religion, the true in faith, and I am not one of the polytheists. My prayer, and my service of sacrifice, my life and my death are all for Allah, the Lord of the Universe, Who has no partner. That is what I was commanded to do, and I am one of the Muslims. O Allah it comes from Thee and is given to Thee from Muhammad and his people. In the name of Allah, and Allah is Most Great. He then made sacrifice.(Abi Dawud)

and

It was narrated that Zaid bin Arqam said: “The Companions of the Messenger of Allah (ﷺ) said: ‘O Messenger of Allah, what are these sacrifices?’ He said: ‘The Sunnah of your father Ibrahim.’ They said: ‘What is there for us in them, O Messenger of Allah?’ He said: ‘For every hair, one merit.’ They said: ‘What about wool, O Messenger of Allah?’ He said: ‘For every hair of wool, one merit.’”(Ibn Majah)

And for all religion We have appointed a rite [of sacrifice] that they may mention the name of Allah over what He has provided for them of [sacrificial] animals. For your god is one God, so to Him submit. And, [O Muhammad], give good tidings to the humble [before their Lord](Quran 22:34)

So pray to your Lord and sacrifice [to Him alone].(Quran 108:2)

Al-Bara' b. 'Azib reported Allah's Messenger (ﷺ) having said:

The first (act) with which we started our day (the day of 'Id-ul Adha) was that we offered prayer. We then returned and sacrificed the animals and he who did that in fact adhered to our Sunnah (practice). And he who slaughtered the (animal on that day before the 'Id prayer), for him (the slaughtering of animal was directed to the acquiring of) meat for his family, and there is nothing of the sort of sacrifice in it. It was Abu Burda b. Niyar who had slaughtered (the animal before the 'Id prayer). He said: I have a small lamb, of less than one year, but better than that of more than a year. Thereupon Allah's Messenger (ﷺ) said: Sacrifice it, but it will not suffice (as a sacrifice) for anyone after you.(Muslim)

Allah Swt and His Messenger knows best.