In Genesis 4 Cain and Abel gave offerings (or sacrifice). Who instructed them to give this offering or sacrifice? Was it a burnt offering?
If my answer here is accepted then I think that would make this a duplicate, though, I would clarify further that we really cannot tell from the text. All we know for certain is that sacrifice is a very old institution and only second in age to marriage and possibly the Sabbath rest.
My original answer to the linked question below for your convenience
It is definitely clear that sacrifice was instituted very early.
Abel and Cain apparently performed sacrifices, Abel bringing animal material and Cain bringing plant material. The ensuing rivalry between the two led to the infamous 'first murder'. It has been argued that Cain knew animal material and animal life was the requirement and his obvious 'cannot be wrong' attitude and jealousy was what led him to murder his own brother.
But did Adam and Eve sacrifice?
One should think that Cain and Abel were told by someone that it was necessary. It is possible that God Himself told them to do so, considering they were also on the same plain speaking terms, demonstrated when God questions and subsequently curses Cain. However, Genesis 3:21 is curious stating just after God declared punishments for the fall:
The Lord God made garments of skin for Adam and his wife and clothed them.
God Himself made the garments for Adam and Eve. Depending on your views of whether there was death before the fall this may or may not be significant. Since you do not specify a tradition I will stick to literal Bible interpretation, in which this view, that there was no death mentioned until this verse, therefore, no death before the fall, is well supported.
So many have hypothesized that God Himself actually performed the very first sacrifice for Adam's and Eve's sins. This site argues that for example. Always leading by example, Adam and Eve then mimicked God's righteous actions and began performing sacrifice. Whether you take this view or not it is indisputable that God approved of the animal's killing so that would leave only Adam or Eve to actually perform the sacrifice. It really does not matter, though, who did it first because just one generation later Cain and Able are sacrificing as if it is a regular thing, showing that it was already instituted and the most likely time was Genesis 3:21. Also, if God did this first sacrifice, He did not do any others, again leaving the task to Adam and Eve.
Now it is not until the reveling of the Law that frequency and reasons for sacrifice were known to us at least. This is more than 1000 years later. It is clear that there were thanksgiving reasons, as Noah did in your example, and it is implied that Cain and Able were performing a possibly annual or other time frame sacrifice as required by God. There are also a few examples of reasons for sacrifice in the story of Abraham. The most notable being told to do so by an angel of God when Abraham was told to sacrifice his own son Isaac. So there may have been very well understood reasons by the ancient persons for sacrifice that may have even been started with Adam and Eve shortly after the fall, but the only indication of those 'rules' becoming written is Leviticus with Moses. It is entirely possible that those sections in Leviticus were only parroting what had been done since the beginning.
So we cannot conclusively say that Adam and Eve started the sacrifice rituals, but the evidence is very heavy that they did and it was ordained by God and likely that He instructed them in it or even did the first one Himself.
The Church Fathers tell us that the idea of offering sacrifice to God was placed in the conscience of man from the beginning:
In the course of time Cain brought an offering of the fruits of the earth to the Lord
Consider how the Lord of nature added knowledge to conscience. After all, who brought this to our understanding? It was none other than knowledge associated with our conscience. The text says, He brought an offering of the fruits of the earth to the Lord [Genesis 4:3]. He knew and understood that he should offer from his own possessions some produce to God as to his master, not because God needs them, but for the purpose of demonstrating his gratitude as being himself a beneficiary of such kindness. God, you see, is proof against need, and depends on nothing we have to offer; but in his ineffable love he shows considerateness for us, and for the sake of our salvation he allows these things to happen so that the knowledge of the Lord may be for the human race a school of virtue.
John Chrysostom (4th c.), Homilies on Genesis, Homily XVIII
The Bible states that the offerings were brought "in the course of time". This suggests only that when the appropriate time for sacrifice had come, both brought offerings. It does not imply a specific command to sacrifice.
We have no idea who taught Cain and Abel how and when to bring offerings to God. They might simply have felt that they needed to give something to God, or maybe their parents told them. The Bible does not say, and anything more would be speculation.
Neither of these offerings are described as burnt. Cain brought fruit of the ground, while Abel brought a "fatty portion" of meat. God preferred Abel's offering, but this wasn't because God did not like fruit of the ground. God specifically told Cain that he (and his plant-based offering) would be accepted if he would only act rightly. (Cain did not listen, though. Not long after hearing this, Cain killed Abel.)
From Genesis 4:
[...] Abel became a herder of flocks, and Cain a tiller of the ground.
In the course of time Cain brought an offering to the LORD from the fruit of the ground, while Abel, for his part, brought the fatty portion of the firstlings of his flock. The LORD looked with favor on Abel and his offering, but on Cain and his offering he did not look with favor. So Cain was very angry and dejected.
Then the LORD said to Cain: Why are you angry? Why are you dejected? If you act rightly, you will be accepted; but if not, sin lies in wait at the door: its urge is for you, yet you can rule over it. Cain said to his brother Abel, “Let us go out in the field.” When they were in the field, Cain attacked his brother Abel and killed him.
Sacrifice is a feature of many non Christian religions, including those such as the Aztecs who had never come into contact with the Hebrew traditions.
Humans have a natural inclination to offer gifts or show their respect to those who are their lords and masters.
Therefore I think it far more likely that the decision of Cain and Abel to make a sacrifice was generated from their own conscious, a feeling that they should show respect by giving something that was theirs.
If God himself or an angel had commanded them to do so, I think the bible would have made that very important point clear.
That god accepted Abel's sacrifice and not Cain's was symbolic of the heart of the giver. Nowadays our sacrifices are in time and money, but the same comment about attitude is still relevant.
So its not the actual item sacrificed that god is concerned about, but how we are thinking when we give it.
It is reasonable to conclude that God did tell them what to offer Him at some point, whether directly or indirectly. This is based on the scriptural points that:
Faith only comes by hearing and by hearing the word of God.(Rom10:17).
Hebrews 11:4 goes on to say
,"By faith Abel offered to God a more acceptable sacrifice than Cain, through which it was testified of him that he was righteous (upright, in right standing with God), and God testified by accepting his gifts."
Putting this into context of Hebrews 11, most if not all heroes of faith mentioned in that chapter had their faith attributed to believing and obeying what God had told. Thus, Abel believed and obeyed the word of God in some way.
Remember without faith (believing and obeying God's word) it is impossible to please God (Heb 11:6). See also (1 Samuel 15:22).
Has the LORD as much delight in burnt offerings and sacrifices As in obeying the voice of the LORD? Behold, to obey is better than sacrifice, And to heed than the fat of rams."
From this one may derive that God was pleased with the obedience of Abel in offering what he had instituted.