Yes, Adam and Eve were most likely vegetarian in the garden of Eden. God gave them all the fruit of the trees to eat in the garden (Genesis 2). But the fall changed everything. At the fall humanity’s relationship with God was broken as was humanity’s relationship with all the animals (Genesis 3).
After the flood, God gave the animals as food for humanity to eat (Genesis 9). Later, the sacrifice of animals and the spilling of their blood for Israel’s sin was to point to fact that a death was needed for God to forgive sins (Exdous 12).
So the death of animals points to 2 facts; there is a break with man’s relationship with the creation he was created to govern; a death is needed to bring humanity back into a right relationship with God. The true death that brought humanity back into relationship with God was the death of Jesus (Romans 5:8-9). The sacrificial death of animals pointed to the death of Jesus and how he has paid for humanities sins. What we need to do is accept his death on our behalf.
Knowing this, is it alright for Christians to eat meat? Yes, because God has given animals to humanity for food. Also Jesus said that all foods are clean, to say that a Christian cannot eat anything is wrong (Mark 7). Christians can eat all foods, because Jesus said so. And Jesus also ate fish after his resurrection and so we know that meat is definitely not wrong for Christian’s to eat (John 21).
For Christian’s food is no where near as important as our relationshp with Jesus. If people do not eat meat but pay no attention to Jesus, then it does not matter what they do, they are displeasing God. It is not wrong to be a vegetartian, it is not wrong to be carnivourous (though very unhealthy), it is not wrong to be omnivourous. But it is very wrong to ignore Jesus.