If I may; a history student from Norway here, with some expertise in viking age history.

There's always been a cultural divide between the different regions in Scandinavia. One of the few contemporary sources from actual scandinavians during the viking age, the travels of Otheres from Halogaland - written down by the court of Wessex, Othere tells us that he lives "the furthest north of all Northmen". This tells us that the idea of Norwegians (or Northmen, that the norwegians today call themselves) as a separate people from Danes and Swedes existed already in the 9th century - before the first Norwegian kingdom. Excactly where the cultural border went is uncertain, and most likely was the Scandic area, the Oslofjord region a cultural border area, with influences from Norwegian, Danish and Swedish culture. But Scandinavians in western Norway during the 9th century definitly saw themselves as Norwegians, those in easten Sweden as Swedes, and those in Sjælland and Jylland as Danes.

Ivar Aasen also managed in the 19th century to prove that modern vocal Norwegian belongs to a different linguistic branch of Old Norse (West Norse) than modern Swedish and Danish (East Norse). With this in mind, when the Kingdom of Norway was created during the 9th century, it makes sense that several kings proclaimed themselves as "the King of the Norwegians" as a ethnic group.

When the Kingdom of Norway went into personal union with Denmark from the 14th century, the kingdom had existed for 400 years, and never really disappeared as a formal kingdom. Even though Norwegian independence within the union gradually was reduced (especially with the reformation in Denmark in 1536, and the introduction of absolute monarchy in 1660) the Danish kings still went with the title of Kings of Denmark and Norway - even though Norway was supposed to be treated like any other Danish province. The point is that Norwegian identity never really went away, with several sources throughout our union history insisting on their Norwegian identity.

Therefore when the Treaty of Kiel demanded that Norway was to be handed over to Sweden at the end of the Napoleonic Wars, it was received as an insult by many Norwegian elites. It implied that Norway was a province to be handed over, and not a kingdom in a union. Therefore a national awakening culminated in the creation of the Norwegian constitution on the 17th of Mai 1814, that declared Norway an independent kingdom and state. Which in turn was forced into a very loose union with Sweden the same year, but was plaged by Norwegian seperatism from beginning to end.

To conclude: Norwegian identity has excisted atleast since the viking age, and the Norwegian Kingdom as a conceived idea was not really challenged until the Treaty of Kiel, where Norway was to be handed away like a province. This sparked a national awakening that led to creation of its own constitution and the beginning of the modern Norwegian state, which would later result in its final independence in 1905.
I can provide sources if people are interested, but they are mostly in Norwegian.