The whole concept of a country as a related group of people from one ethnicity or historical origin is relatively recent.
Feudalism did not have this concept; a country was the land belonging to a king (or equivalent), mediated through a set of nobles. There was no concept of illegal or legal immigration; the population of a country were the people who worked for, or were owned by, the nobles ruling that country. There were land rights granted to peasants who had historically lived in that place, but these could and were often overruled by nobles.
European nobility had no such idea of ethnicity or national grouping; the English monarchy is a German family, and most of European nobility were related to each other much more closely than to the citizens of their country.
Early post-monarchy states didn't have this concept. The English Civil War and the French Revolution didn't create states that had a defined concept of the citizen as a member of any ethnic grouping. Again, there's no mention of immigration in any of the documents from this period. It just wasn't a concept they thought about.
The whole concept that a nation-state is a formalisation of a historical grouping of ethnically related people is a very recent one, only a couple of hundred years old.
So to answer your question: It is very easy to have a sovereign country without a policy that prevents unfettered immigration; you just don't care about your population being ethnically diverse. Your citizens are the people who live in your country, and have undergone whatever ceremony and formality you decide makes them citizens.
This is, after all, how America historically did this; if you arrived in America and pledged allegiance, you became a citizen of America.