Consider Genesis 9:3,
"Every moving animal that is alive may serve as food for YOU. As in the case of green vegetation, I do give it all to YOU."
If the eating of animals as food was already in practice, there would have been no need for God to have even said this.
By saying, "I do give it all to YOU" suggests that at that point, both of these options of food were now available when one option wasn't before.
Other Bibles echo this suggestion:
"Every moving thing that lives shall be food for you; and just as I gave you the green plants, I give you everything." (NRS)
"Every moving thing that lives shall be food for you; and as I gave you the green plants, I give you everything." (RSV)
"I have given them to you for food, just as I have given you grain and vegetables." (NLT)
Conditions Attatched to The Eating of Meat
God states that the soul (life) of the fleshly creature is in the blood and is therefore sacred to Him. (Le 17:11-14) Not only is eating blood prohibited in the Old Testament, but also in the New Testament the governing body of the early Christian congregation restated this prohibition, forbidding the eating of animals strangled or not drained of blood:
"That you abstain from ...blood." (Acts 15:29)
As has been addressed, originally, vegetation and fruit, and not flesh, were given man as his diet. But after the Flood, God added animal flesh, commanding, however, that "flesh with its soul—its blood—you must not eat." (Gen. 9:3, 4)
So God commanded that, before eating the flesh of an animal, his people were to pour out its blood on the ground and cover it with dust, being careful not to eat the blood, on pain of death. (Deut. 12:23-25; Lev. 7:27)
The eating of flesh by Christians is proper, but the apostle Paul pointed out that flesh is not absolutely essential to man as food when he said that if his eating of meat was a source of stumbling to other Christians, he would "never again eat flesh at all." - Rom. 14:21; 1 Cor. 8:13.
God Himself told us that we could eat meat from "every animal". "Every moving animal that is alive may serve as food for YOU." (Gen. 9:3)
So when someone carefully takes the strict precautions that God outlined by making sure that an animal is properly bled before consumption, they wouldn't be breaking God's command of eating blood. Since God Himself has issued these directions, obviously, if properly done, God does not have a problem with eating the meat from "every animal". Additional Reading: Should Christians Eat Red Meat Since it May Contain a Trace of Blood? (Search For Bible Truths)
Blood - Links to Information (Defend Jehovah's Witnesses)
Meat - Links to Information (Defend Jehovah's Witnesses)