The Rambam writes in Hilchos Melachim 9:1 that Adam HaRishon was commanded in six mitzvos, and Noach was commanded in a seventh. Adam was commanded to not do the following: worship avodah zarah, curse Hashem, kill, gilui arayos, and steal. He was also commanded to set up a court system. In addition to those commands, Noach was commanded not to eat from ever min hachai (a limb detached from a live animal).
The Gemara in Sanhedrin 59b says that Adam was forbidden to eat any of the animals. He was only permitted to eat fruits and vegetables. He was therefore not commanded to not eat ever min hachai since he was not allowed to eat animals at all. The reason why the Rambam did not mention this prohibition is because it was not intended to last forever. Only after the mabul did Hashem permit Noach to eat animals, as the pasuk in this week’s parshah says: “kol remes asher hu chai lachem yiheyeh le’achlah” (Bereishis 9:3). Prior to this it was forbidden to kill an animal in order to eat it.
We find that Noach brought korbanos immediately after he exited the teivah, prior to being allowed to eat animals. Additionally, we find that in Parshas Bereishis, Hevel brought korbanos from animals although he was not allowed to eat them. The Gemara in Avodah Zarah 8a says that Adam brought korbanos as well.
Several Acharonim were bothered by a question (see Zera Avraham, end of siman 13). The Gemara in Menachos 6a says that a korban must be brought of something that may be eaten. This is referred to as “mashkeh Yisrael.” How could Noach, Adam, and Hevel have brought korbanos from animals that they themselves were forbidden to eat?
According to Tosafos (Sanhedrin 56b d”h achal), Adam was allowed to eat animals; he only was forbidden to kill an animal in order to eat it. However, if an animal would die on its own, he would be permitted to eat the animal. Based on this opinion, the question does not start because the meat of an animal was not forbidden to be eaten; rather it was only forbidden to kill an animal in order to eat it. But the Acharonim point out that the Rambam seems to disagree with Tosafos with his belief that Adam was forbidden to eat an animal even if it would die on its own. They imply this from the fact that the Rambam says that ever min hachai was only first commanded to Noach. The reason why it was not commanded to Adam is because he was forbidden to eat all animals. According to Tosafos, Adam was already forbidden to eat ever min hachai.
Some Acharonim suggest that the halacha of mashkeh Yisrael does not apply to a ben Noach who is bringing a korban. Thus Noach and Hevel did not have to bring korbanos from items that they could have eaten themselves. Others suggest that the halacha of mashkeh Yisrael only applies to korbanos brought on the Mizbeach. Even according to the opinion that Noach brought his korbanos on the place where the Mizbeach would later be built, it did not have the status of the actual Mizbeach.
I would like to suggest another answer. The halacha of mashkeh Yisrael requires that all items brought as a korban must be fit for consumption. However, if one ate hard cheese and cannot eat meat for six hours, he would nonetheless be permitted to bring a korban of animal meat. Similarly, one would be permitted to bring a korban on a fast day, when it is forbidden to eat anything. The reason for this is because in these cases the food is not forbidden in and of itself; rather, it is the person who cannot eat the food at that time.
I believe that the prohibition that existed prior to Hashem allowing Noach to eat animals was similar to that of a fast day, whereby the food was not intrinsically prohibited – only that the people could not eat it at that time. We do not find that Hashem changed something from being a non-kosher or forbidden food to becoming one that is permitted anywhere else. It is therefore likely that this prohibition was not intrinsic. Animals were never deemed as non-kosher for bnei Noach. They were simply not allowed to eat them, for it was as if it were a fast day regarding eating animals.