The question was not whether Jesus was a vegetarian or whether God told Peter to slaughter animals and eat, but whether Adam and Eve were vegetarians. What is more important that the OP's question however, is what God is trying to teach us through these Hebrew stories in the Book of Genesis.
**God also said: "See, I give you every seed-bearing plant all over the earth and every tree that has seed-bearing fruit on it to be your food; and to all the animals of the land, all the birds of the air, and all the living creatures that crawl on the ground, I give all the green plants for food." And so it happened. (Genesis 1:29-30)
God clearly gave the plants, trees and fruit to Adam and Eve and to the animals for food. Scripture does not say whether Adam and Eve killed animals and ate them but it is clear that God gave Adam and Eve plants specifically and explicitly.
**Abel became a keeper of flocks, and Cain a tiller of the soil.* (Genesis 4:2)*
We see that Abel was a shepherd, but that could have been for animal products such as wool and milk, and not necissarily meat. After the flood however, God said something very imporant to Noah.
**Dread fear of you shall come upon all the animals of the earth and all the birds of the air, upon all the creatures that move about on the ground and all the fishes of the sea; into your power they are delivered. Every creature that is alive shall be yours to eat; I give them all to you as I did the green plants. *(Genesis 9:2-3)*
God said that as he had explicitly given mankind plants to eat in the past, so he was now doing with the animals. So it would appear that God's original intent was that man not eat meat. Again however, whether Adam and Eve were vegetarians or not and when man first started eating meat gives us the literals sense of scripture, but what is much more important to us as Christians are the spiritual senses of scripture, how the stories point us to Christ and how they teach us to live our lives as followers of Christ and children of God.
The order which God creates things in Genesis 1 is important. Plants first, then fish and birds, then beasts, then man created in God's own image. The order in which God creates things tells us it's order of importance in creation and who has dominion over whom, and who serves whom. Creation is God's gift to man and serves man but man is to care for creation. In creating man last, we see that man is to serve God and God is to care for man. That is God's original plan.
But we fell, and the order in creation was wrecked. God however, has a plan to reestablish his original order, and after the fall God starts implimenting his plan.
The story of Noah is what I call the "Third Genesis". It is a third creation story.
In Genesis 1:2 a mighty wind sweeps over the waters, and in Genesis 1:9 God gathers the water into a basin so that dry land appears. The same thing happens in Genesis 8 when God remembers Noah in the ark and causes a wind to dry up the water so that dry land appears. There is a direct paralel here. Then God does something unique; God enters into a covenant with Noah.
Covenants create family bonds, and God the Father makes the first coveannt with man, bringing him into his family as his son. This is the first step in God's plan to restore man to his original place at the top of creation in the image of God, the first step in God's plan to restore the natural order of creation. God makes a covenant as the first step in restoring man to his original condition before sin etered the world.
But man is fallen. Remember that. The covenant can only do so much because man has lost his original integrity, "Walking with God", caring for creation which was God's gift and serving God who is his creator. Man lost that.
Part of the "Third Genesis" of Noah and the ark is God calling Noah to care for the animals on the ark. This is God teaching man to do what Adam and Eve did in the garden before sin entered the world - they cared for the garden and ministered to creation in service to God who gave it to them as a gift. In calling Noah to care for the animals, God reminds man that creation is a gift and man is to care for creation.
And in giving man the animals to eat, God sets about restoring the original order of creation. Remember here that man was fallen. The order of creation was totally wrecked. The world was a viscious and evil place after the fall. Cain killed Abel. People engaged in incest, cannibalism, bestiality, sold their own daughters into slavery, and sacrificed their infants to false Gods. The world was so viscious and evil that God wants to start all over again, and he says as much to Noah as he begins to instruct Noah on the building of the ark.
**When God saw how corrupt the earth had become, since all mortals led depraved lives on earth, he said to Noah: "I have decided to put an end to all mortals on earth; the earth is full of lawlessness because of them. So I will destroy them and all life on earth. (Genesis 6:12)
Then after Noah passes through the flood, God commences his plan to restore the original order of creation. He causes the dry land to appear just like in Genesis 1, and restores the most basic order of the relationship between plants, animals, man and God, making animals fear man and giving them to man as food while entering into a covenant with man and thereby creating a father-son relationship between himself and man.
The literal sense of scripture - whether Adam and Eve were actually veegans before the fall - is important only insofar as it points us to what God is trying to teach us about himself and ourselves and our relationship with him - the spiritual sense of scripture.
That's how Hebrew storytelling works. The facts are not as important as what the facts are telling you about relationship, about cause and effect, about family bonds, about blessing and curse, about life and death, about our responsiblities as children of God, and about how we can trust God as a Father.
The literal sense is only important insofar as it leads us to the spiritual sense, and how we are supposed to be children who trust God the Father, and how God the Father loves us so much as to set in motion a plan to restore the natural order of creation for our own good.