A practical question frequently asked is: can I buy and eat meat from a supermarket or regular butcher shop, or should I buy kosher slaughtered meat, or maybe become vegetarian?
In Genesis, we read that to Adam, the green herb was given to eat.
וַיֹּ֣אמֶר אֱ-לֹקים הִנֵּה֩ נָתַ֨תִּי לָכֶ֜ם אֶת־כׇּל־עֵ֣שֶׂב ׀ זֹרֵ֣עַ זֶ֗רַע אֲשֶׁר֙ עַל־פְּנֵ֣י כׇל־הָאָ֔רֶץ וְאֶת־כׇּל־הָעֵ֛ץ אֲשֶׁר־בּ֥וֹ פְרִי־עֵ֖ץ זֹרֵ֣עַ זָ֑רַע לָכֶ֥ם יִֽהְיֶ֖ה לְאׇכְלָֽה׃
G-d said, “See, I give you every seed-bearing plant that is upon all the earth, and every tree that has seed-bearing fruit; they shall be yours for food. (Genesis 1:29)
The opinion of the Rambam  is that Adam was not permitted to eat meat. The opinion of Rashi  is that Adam was permitted to eat meat, but only from an animal that had died a natural death, but he was certainly not permitted to eat any part of a living animal.
After the flood, Noah received permission from G-d to kill animals for food.
וּמוֹרַאֲכֶ֤ם וְחִתְּכֶם֙ יִֽהְיֶ֔ה עַ֚ל כׇּל־חַיַּ֣ת הָאָ֔רֶץ וְעַ֖ל כׇּל־ע֣וֹף הַשָּׁמָ֑יִם בְּכֹל֩ אֲשֶׁ֨ר תִּרְמֹ֧שׂ הָֽאֲדָמָ֛ה וּֽבְכׇל־דְּגֵ֥י הַיָּ֖ם בְּיֶדְכֶ֥ם נִתָּֽנוּ׃
The fear and the dread of you shall be upon all the beasts of the earth and upon all the birds of the sky—everything with which the earth is astir—and upon all the fish of the sea; they are given into your hand.
כׇּל־רֶ֙מֶשׂ֙ אֲשֶׁ֣ר הוּא־חַ֔י לָכֶ֥ם יִהְיֶ֖ה לְאׇכְלָ֑ה כְּיֶ֣רֶק עֵ֔שֶׂב נָתַ֥תִּי לָכֶ֖ם אֶת־כֹּֽל׃
Every creature that lives shall be yours to eat; as with the green grasses, I give you all these. (Genesis 9:2-3)
The following two reasons, among others, are given as to why man was allowed to eat animals;
(1) The animals survived the flood only because of Noah’s efforts. Because they owed their lives to him, Noah and his descendants had acquired rights over them – including the right to consume them Ramban (1:29).
(2) Man was weaker after the flood (as evidenced by his shorter life span). The world’s flora was of lower quality than that before the flood. The world would now have seasons, with long unproductive winters. Man would also spread further – to colder areas of the earth. As a result, he would need meat to survive (Malbim, R. Hirsch). 
Although Noah was permitted to kill animals, it is appropriate for a man to take pity on animals and kill them in the most painless way possible. After all, a man was not given unlimited permission to make a living being to suffer. Moreover, it is fitting for a human being to distance himself as much as possible from cruelty.  Not only in the killing of animals but in his entire dealings with animals. We should not inflict pain or suffering on them unnecessarily in any way. This falls under the commandment which in Hebrew is called Tza’ar ba’alei Chayim and also applies to Noahides. 
In allowing the eating of meat, restrictions were also given. Noah, and thus to mankind, was not permitted to use meat that was removed from domesticated or wild mammals and birds, while they were still alive.
We can learn this from Genesis 9:4 which states:
אַךְ־בָּשָׂ֕ר בְּנַפְשׁ֥וֹ דָמ֖וֹ לֹ֥א תֹאכֵֽלוּ׃
You must not, however, eat flesh with its life-blood in it. 
There is no minimum amount that a Noahide must consume to incur liability for Eiver min ha-Chai. Even the smallest amount of – an edible part of an animal – Eiver min ha-Chai is enough to incur punishment. However, swallowing an entire living creature is not prohibited. After all, the prohibition only applies to meat that is “from” a living creature.  
Returning to the initial question: is it okay to eat meat from the supermarket? After all, you don’t know if the meat comes from an animal that is still alive. The moment you buy the meat you can be sure that the animal is dead. (Unless it is Rocky Mountain oysters, for example). And the sages point out that it then no longer falls under the prohibition of Eiver min ha-Chai. Once the animal dies, eating the flesh that was taken from it does not incur the liability of a capital sin. However, the sages added a prohibition that meat removed from an animal while it was living remains prohibited for everyone for all time – even after the animal has died:
Flesh that becomes detached from it [while it is dying] is considered like flesh detached from a living creature and is prohibited to a Noahide even after the animal has expired. 
The problem in modern slaughterhouses is that the animals are stunned by electric shock before they are killed. However, although the animal appears dead – because it is not moving or because it has stopped breathing – it does not mean that the heart has permanently stopped pumping. However, in proper practice, there is enough time after the actual slaughter that the heart has permanently stopped before any meat for human consumption has been removed. 
It is permissible to buy meat in the ordinary supermarket. Two reasons may be proposed to give this leniency, namely Safek (doubt) and Rov (majority).
Safek here means that there is more than a 50% doubt about whether the piece of meat is Eiver min ha-Chai. Rov here means nullification of a forbidden substance that is mixed with a majority of an indistinguishable permitted substance. If a prohibited item is mixed with a majority of permitted items to the point that we cannot distinguish between the two, then for some types of mixtures, the prohibited item is considered “nullified” in the majority. However, there are differing Rabbinical opinions (some stricter and some more lenient) as to which (if either) of the above points apply to Eiver min ha-Chai that might be eaten by Noahides.  
Knowingly eating meat of a live animal is punishable.
Eating meat from an animal that was not yet dead at the time it was severed is prohibited after the animal dies, but not punishable.
Meat from the supermarket may be bought and eaten by Noahides.
There are Noahides who choose not to buy meat from the supermarket because they do not want to have a small risk of eating meat that is forbidden (not punishable anyway). They consciously choose to eat only certified Kosher slaughtered meat. When they take on this strictness – which is not mandatory – it may become forbidden for them to revert to eating non-Kosher meat, if they did not state that they are taking on this extra stringency “without a vow”. They can eat out at a restaurant, but they are not allowed to eat food there that contains real meat. 
By Angelique Sijbolts
 Sefaria see Rambam – https://www.sefaria.org/Genesis.1.29?lang=bi&with=Rashi&lang2=en
 ] Rashi on Tractate Sanhedrin 57a – 4 https://www.sefaria.org/Sanhedrin.57a.4?lang=en&with=Rashi&lang2=en
 Genesis 9:2-3
 Meat After the Flood
 ] The Divine Code 4 edition p. 238
 Sefer Chassidim 666
 Genesis 9:4
 The Noahide Laws p 349 referring to Maimonides, Hilchos Melachim 9:10. and Chullin 102b
 The Divine Code 4 edition p. 243
 The Noahide Laws p. 350 referring to Chullin 121b
 Own research and interviews at local slaughterhouse
 The Noahide Laws p. 353
 The Divine Code 4th edition, Part IV, Chapter 6.
 The Noahide Laws p. 355
Thanks to Dr Michael Schulman and Rabbi Tani Burton for the feedback