The seeds of the idea of nationalism date to the Peace of Westphalia, but few of us would actually think of the Westphalian "states" as nations in the modern sense.
I'd date the modern nation-state to:
The American Civil War. (1865). There's a reason why this is called "The War Between the States" in the South - before the Civil War, it wasn't clear whether the U.S. was a loose confederation that any state could secede from at will, or a unified political body that would fight to maintain its integrity.
The unification of Germany (1871). This is geographically the same area as the Westphalian states, but people think of "Germany" as the nation, not Munster/Brandenburg/Westphalia/Saxony/etc.
The unification of Italy (1871). Again, we don't think of the Papal States as a nation, we think of Italy as one.
The Meiji restoration in Japan (1868), where decentralized power under the shogunate was centralized under the emperor.
Russification under Alexander II of Russia (1859-1882), which included both the emancipation of the serfs and a systematic campaign to promote the Russian language & culture within territories governed by the Russian empire.
The issue is that territories often shifted hands, and what territories happened to be ruled by the same people often boiled down to which monarch happened to inherit or conquer which areas.
There simply was no clear unified concept of a nation of people.
The rise of the national states came in part as a result of Romantic Nationalism (or Nationalromanticism) [1], and the wave of revolutions that swept Europe in particular as a reaction against the above:
For the first time there was the rise of the sentiment that certain areas belonged to certain states because their people belonged together due to common language or culture, rather than because the territories were owned by a specific monarch, or because of a given convenient political association.
This coincided by wholesale creation of cultural mythos. E.g. Norway had not existed as an independent kingdom since 1380, and had only existed as a unified kingdom for a few hundred years at that time. But with the rise of Romantic Nationalism, authors and artists and politicians contributed to creating a mythos of a Viking era Norway and Norwegian people that had a common destiny.
Norway was nothing special in that respect - it is one example of dozens in Europe alone where nations were spun out of mythology or ideas about a shared history or destiny that largely boiled down to finding convenient political or language boundary and creating a mythos that fit them.
I'd date the modern nation-state to:
The American Civil War. (1865). There's a reason why this is called "The War Between the States" in the South - before the Civil War, it wasn't clear whether the U.S. was a loose confederation that any state could secede from at will, or a unified political body that would fight to maintain its integrity.
The unification of Germany (1871). This is geographically the same area as the Westphalian states, but people think of "Germany" as the nation, not Munster/Brandenburg/Westphalia/Saxony/etc.
The unification of Italy (1871). Again, we don't think of the Papal States as a nation, we think of Italy as one.
The Meiji restoration in Japan (1868), where decentralized power under the shogunate was centralized under the emperor.
Russification under Alexander II of Russia (1859-1882), which included both the emancipation of the serfs and a systematic campaign to promote the Russian language & culture within territories governed by the Russian empire.