Germany and Italy are mainly what I have in mind with this post. There was not a nation of Italy or Germany until reletively recently, but there was complex regional powers that overlaped in territory and influence like the Papal states, Holy Roman Empire, etc. So when did people think of themselves as Germans and Italians, or other modern European country rather than Prussians, Florentines, Bohemians, etc.
The idea of national identity can date back centuries, however from a more modern (using your given dates) perspective the answer is around the end of the Thirty Year War.
In "Traditions and Encounters: A Global Perspective on the past" by Jerry H. Bentley and Herbert F. Ziegler, the contribute the modern European state identities to the Peace of Westphalia. For it lead to the idea of statecraft, and that countries could bind together and rule themselves autonomously.
Many of these areas had similar cultures, like the German speaking states in the Holy Roman Empire. However, some of these would come together as a result of military power, combining to protect a common shared homeland, marrying of royalty, or because they were simply taken over. For example, in the Dutch Republic (1581-1785) formed due to was formed because they opposed the rule of Spanish King Philip II of Spain.
Many other nation/nation states would be forged due to this shared sense of brotherhood, or from simply being conquered
However, the modern countries (within the last 100 years) would come from WWII, when many of the empires established throughout the 18th and 19th century would begin to break down due to the very same ideas of a will for autonomy and a shared culture, history, and or language.
(This may or may not be a complete answer/the desired answer, please ask follow up questions if needed)
Sources:
Traditions and Encounters: A Global Perspective on the Past (5th Edition) by Jerry H. Bentley and Herbert F. Ziegler
Introduction to Global Politics (3rd Edition) Steven L. Lamy, John S. Masker, John Baylis, Steve Smith and Patricia Owens