So to answer your question we first need to define how the 1648 Peace of Westphaila defined the 'nation-state'. According to Elizabeth Cobbs-Hoffman the biggest thing that Westphalia did to the European Order was dismantle the idea that a nation derived sovereignty from some higher temporal authority, usually idealized as an Emperor. This was a hold over from Roman times and indicative of the role that Roman law played in European politics. The role of the Emperor was carried out by the Pope and the unifying force of the universal Roman Catholic Church. The Wars of Religion removed this unifying force.

As a result, the Nation-State would be supreme, receiving its sovereignty from no outside force. The Westphalian system had three key tenets:

First, states had a fundamental right to self-determination; second, all states were legally equal; and third, no state would violate territorial integrity. Within societies...there must be "an authority capable of commanding all the members...and of compelling those who should refuse to obey." But between nations, sucha n idea was tyranny. Every sovereign state, to be a state, must "possess an absolute independence."

Now, to answer your actual question.

Today we tend, especially in the United States, to think of "Nation" and "State" as essentially synonymous (probably in the US because "state" has a particular political meaning). This was not always the case. A Nation used to refer to a "people," often in an ethno-linguistic sense but not necessarily, regardless of their political organization. A State was that organization. So, a so-so example: In the 18th century there was a "German Nation" but not a "German State". The theory of the "Nation-State" is that every Nation, in the ethno-linguistic sense, should have its own State, in the political sense. In practice this doesn't always happen with some very well known examples. In some cases rulers have self consciously defined themselves as leading the Nation as opposed to the State (for example Napoleon was Emperor of the French (Empire des Français) to distinquish himself from from the King of France (Roi de France).

Well, Benedict Anderson argues that 'nationhood' as a concept is a product of modernity - specifically, print capitalism. See also Hobsbawm & Ranger on Invented Traditions. Their work is Eurocentric, but in general sovereignty prior to that would have been, as the name suggests, linked to the sovereign that served as the representative of the people and sometimes religion.

James Scott also talks about how SEA kingdoms defined their extent of rule by manpower- how many men they could command in a pinch, rather than territorial boundaries that would naturally shift according to the seasons.

tl;dr insofar as nationhood existed in antiquity, it was probably more as a ethnic/racial identification or in reference to the lineage of a sovereign.