As a bonus were national anthems a result of something particular? Was there a 'thing' that caused them or did they more or less evolved? If I would have been born in 1769, would I have had a concept of a national anthem? What would be a good date for the former question?
If you had been born in 1769, no you probably would not have been familiar with the concept of a National Anthem. At least not until you got quite old.
Wikipedia has a nice entry on National Anthems, wherein you will find that they "rose to prominence in Europe during the 19th century". Poking around a bit, it looks like the timing is more like the very late 19th century to the early 20th.
Perhaps a better clue is with the tag on this question: Nationalism. It turns out that Nationalism itself was a brand new concept in the 18th century (the term was invented by a man born in 1744). It didn't really become prevalent until the mid 19th. It would probably be difficult to even conceive of a "national anthem", without a popular conception and affection for the nation.
Actually, the oldest national anthem in the world is the Dutch Wilhelmus, which dates back to the Dutch revolutionary war, being composed in 1574, with the text being even older, having been traced back to at the latest 1568.
It was not designated as such however until 1932, but had been the de-facto national anthem since that time, including being used on official occasions like crowning of kings and queens.
http://en.wikipedia.org/wiki/Wilhelmus has details.
Arguably the first national anthem was France's La Marseillaise in 1792. It was the symbol of revolutionary France against the monarchies of Europe. The title was a reference to a detachment of soldiers from Marseilles as they marched into battle.
The (translated lyrics) of the first verse exemplify the newly recognized sentiment of "nationalism."
"Arise, children of the Fatherland,
The day of glory has arrived!...
To arms, you citizens,
Form up your battalions,
Let's march, let's march!
So that the impure blood
Will water our soil."
The answer to your question depends on what exactly you consider to be an “official” national anthem. However, a case can be made for the priority of “God save the King”, first performed in 1745.
Second place probably goes to the Marseillaise, which was officially adopted as the hymn of the French Republic in 1795.
In the same year (1795) the great Austrian composer Haydn returned home from a long stay in England, where he had been much impressed by the fact that the English had such a sprightly national hymn, so much so that in 1797 he composed a national (or imperial) hymn for his own country, setting a pre-existing text (“Gott erhalte Franz den Kaiser”). This is still the Austrian national anthem.
In 1841 the German nationalist poet Hoffmann von Fallersleben took Haydn’s melody as the basis for his Deutschlandlied (“Deutschland, Deutschland über alles”). This did not officially become the German national anthem until 1922, when it was elevated to that rank by the Weimar Republic. It remains the German national anthem to this day (though the atrocious first verse is not normally sung in public at present).
You can find some more information in the wikipedia article "Deutschlandlied", more detailed in the German version.