Part of the problem with your question is that it is very difficult to define 'the state'. The commonly quoted definition Weber uses is a 'territorial monopoly on legitimate violence', but this seems to almost be synonymous with 'society', and some of the examples one might use of a stateless society (e.g. Catalonia during the Spanish Civil War) definitely had 'a monopoly of legitimate violence', but that monopoly was held by institutions that don't really look like 'the state'. A rough and ready definition of the state is a centralised, hierarchical military and bureaucratic organisation that exercises control over a territory. This seems to capture early predator states as well as the modern nation state, the crucial difference being that the modern nation state has far more additional machinery attached to the 'bureaucratic' bit (schools, centres for disease control, etc.).

The most obvious example of a large society without such a thing is, as mentioned, Catalonia during the Spanish civil war. The second largest trade union in Spain and the largest in Catalonia in 1936 was the anarcho-syndicalist CNT (national workers confederation), who believed in creating a modern, industrialised but stateless society controlled democratically by the working class. When the fascist general Franco launched a coup in July 1936, the centre-left Republican government effectively dissolved overnight, and it was only the initiative of the working class organised largely within the CNT that prevented a fascist takeover. Because the working class suddenly found themselves in control of society, and in Catalonia were organised through the CNT, they set about running society in a stateless way - with mass assemblies of workers making most of the administrative and economic decisions. The 'state' in the definition we used earlier reconstituted itself in Madrid on the republican (anti-fascist) side, and in the 'may days' in 1937 that state took control of Barcelona away from the CNT and set about re-establishing state authority across North-Eastern Spain, before ultimately losing the war to Franco. If you are interested in a modern industrialised society being run in a stateless way, this is definitely the place to look; there are ongoing debates about how anarchist Catalonia actually functioned and to what extent it was truly 'stateless' or 'democratic'. Othere possible examples of large stateless societies (although not of a million or more) are Çatalhöyük and Teotihuacan, although it is important to stress that this is all contested territory academically speaking.

If you are interested in further discussions of the question in prehistory, Graeber and Wengrow's excellent 'The Dawn of Everything' discusses this question in great depth, and is the main source I am drawing on for discussion of the Indus River Civilisation.

lFor the Spanish civil war sources are too numerous to count. George Orwell's 'Homage to Catalonia' is an excellent and highly readable primary source. For secondary literature I really like Guilamon's 'The Friends of Durruti Group: 1937-39' or Mompo's 'Was there a Spanish revolution?'

OP, u/ozymandias911 touched on this, but it may be worth drilling down some to determine exactly what you mean by "state" or, alternatively, which common element of the modern state you're looking for examples of people doing without. Are you interested: in mass democracy without intermediating (i.e. representative) institutions? collective action without the use of coercive force to ensure norm adherence? "private" methods of dispute/conflict resolution? concepts of property rights without bureaucracy?

large-scale stateless society

It is more of a question related to political science.so I can answer this. When you use the word ' State ' you are distinguishing other forms politically organized Society throughout human history. The notion of formation of state is closely related to the transition period between feudalism to industrial capitalism. In this period the rise of absolute monarchy led the annihilation of semi autonomous authorities in a certain geographical area , where that particular monarch had power. Three things happened in this period 1. State started to monopolize the legitimate use of violence 2. State started to extract resources from agriculture sector to industrial sector 3. State used propaganda to construct a social and political identity to define the notion of "US" . That is why early state were national state not nation state (Charles Tilly) . Now when someone someone says stateless Societies it means people are not part of this politically organized units which came into being after 16th century.

James C Scott work ' the art of not being governed ' is good example of real academics work on stateless society. Otherwise as John Agnew has argued that in academics our thinking are restricted to ' territorial trap ' . Later vinit thakur and other post positivist thinkers also contribute to this particular tradition. So coming back to Scott , his work is on Zomia people. Zomia people's history are not part of any state history. They have their own history , events and social norms , around which they organized themselves. If you are interested in more perspective on Stateless and project of state you can read writings of vinith thakur and James C Scott.