What would be the smallest amout of general ethnic groups that would encompass everyone?

Looking at a list of world ethnicities there are dozens but if we narrowed it down to broader categories how many would we need?
-European
-Asian
-African
-American indigenous
-Australian indigenous
Would everyone fall under one of these categories?

Latin Americans are going to be problematic since they are a blend of so many other ethnicities. But I’m not sure I understand your question. You could start out with Africans and non-Africans and then go from there.

Human?

Depends on the range. Where do Polynesians fall in those categories? Andaman Islanders (who appear to have been isolated for millennia). Are Arabs “Asians” or “Africans”? What are Filipinos? Are Turks Asians or Europeans - does this depend on which side of the Bosporus they live?

Most people recognize several different ethnic groups that are often bunched together as Africans. The Bantu, the Nilotes, and the Khoisan are as distinct from each other as they are from Asians or Caucasians. And the indigenous inhabitants of Madagascar are more connected to the native people in Australia than those in Africa.

Once you get out of very closely-related cultures there’s no accepted consistent or meaningful way of categorizing ethnic groups into super-groups, and our standard societal classifications of ethnic groups have almost no correlation to the biological relatedness of the groups in question, so I think this is kind of a fool’s errand. Maybe if you are willing to accept classifications in which any one group may fall into more than one super-groups, but even then the question of “how many super-groups are there” has no clear answer.

You can use those, but they’re meaningless and arbitrary. Where do the various peoples that live in the Middle East fall and why? How about the Indian sub-continent? You can call them Asian, but how closely are they related to the Han Chinese? Would you call them European and why?

You first have to explain what the categories represent before you can classify people into them. What does it mean to be African in this context? Why would Berbers and Tutsi be considered in the same category? If you dislike that classification, lumping Berbers and the Sami together in European is just as bad.

Bushmen …

See Wikipedia article San People

Ethnicity is a social construct, and as others above have noted, its pretty arbitrary. If Serbs and Croats can identify themselves as different ethnic groups, then we are not far short of separating Mormons and Mennonites or … [just forgot the other good alliterative one].

We tend to put skin colour, language and religion high on the list of factors we separate ethnicity on, but in largely homogenous societies it can fall on other factors - like 3rd gen Koreans in Japan being ‘ethnic’, but primarily because they are excluded from mainstream society as not quite Japanese enough.

Usually ethnicity is part self-identity paired with separation and othering from another group. Which came first is debatable.

Caucasian
African
Asian

I think those would be the smallest groups you could break people down into?
That encompasses everyone.

Australia’s Aboriginal people, among others, just gave you a withering look of contempt.

So are Egyptians African or Caucasian? Are Indians Asian or Caucasian? Are Australians and New Guineans Asians? Are Turks Asians or Caucasians? Are Native Amiercans Asians? Are San Africans?

Sure, we can categorize people by the continent they live on, or the continent their ancestors lived on, but continents aren’t reproductively isolated populations, as the demographic changes in the Americas over the past 500 years have shown. And those sorts of demographic changes happened in the further past, they just aren’t nearly as well documented.

Three main genetic clusters are Eastern (subdivided into Australian-Papuan, East Asian, Native American), Eurasian, and (Subsaharan) African. Three small outliers (Bushman, Pygmy, Hadza) may be separated from African. Of course “hybrids” occur, e.g. Cape Mixed Ancestry with genome roughly between Eurasian and African.

Genetic clusters aren’t ethnic groups. As ill-defined as the original question is, OldGuy has provided the best factual answer you are going to get.

Again, most of Latin America is not going to fit into that classification scheme. That’s a lot of people. You have some small number of pure Native Americas, pure Europeans, pure East Asians, but mostly every mix of those you can imagine with a whole bunch of sub-Saharan African thrown in for good measure.

Per Wikipedia, North Indians are definitely Caucasians while South Indians are uncertain (Dravidians)

Link - See map under classification Caucasian race - Wikipedia

That’s also per “19th century classification”, if you read the article. Not very useful, even in the not-useful world of race characterization.

Does that include Neanderthals and Denisovans?

Seriously, even the concept of distinct species breaks down when dealing with ring species or groups like closely related species of the Tanagers. The notion of clear distinctions in ethnic groups–a human invention governed as much by culture and linguistics as by genetics or cladistics–does not hold up to scrutiny under careful examination. Humans have been travelling, trading, and fucking since multiple groups left the plains of Africa for distant lands, and trying to divide the population into discrete groups will inevitably result in fuzzy boundaries. I defy you to tell me which group Rosario Dawson or Bruno Mars falls into, and I think Zoë Kravitz transcends racial and species barriers to become the first transhuman by the force of shear allurement.

Stranger

Exactly zero of these categories are “ethnic groups.”

The fuzziness of these group definitions gives us a pretty good rule-of-thumb indicator: people who rely on them for drawing meaningful conclusions are at best naive, at worst nefarious.