Is there any evidence that a ‘natural’ language that exists today was created by somebody a thousand (or two) years ago. And that it evolved till today?
Possibility? Of course, there is always a possibility, but rather remote one, if you mean a full featured well-known modern language.
The best candidates are "taboo languages", where the lexical items are replaced because of taboo/religious pressure. Perhaps the best known is Dyirbal, where a special version of the language is to be used in front of "tabooed" persons.
Though it probably does not go millennia into the past, and it's questionable if it should be considered a language, since it is just a vocabulary encoding.
Yes, the Damin language (Wikipedia article), a ceremonial language and only natural click language outside Africa, was probably constructed.
People learn languages from other people who speak them. If someone ever got others to adopt his language as their "natural language," they would have had to learn it from him. Without a community of speakers, it would have been impossible for this to happen. At some point we have to account for the fact that someone would have had to design the language and actually teach it to others.
I believe that this has never happened in recorded history. We do indeed find that an early Greek philosopher named Pherecydes invented an "artificial" word for "table":
He maintained that the divine name for "table" is θυωρός, or that which takes care of offerings. (Diogenes Laertius 1.119)
There is no evidence for anyone ever having invented an entire language, which would certainly be much more notable.
This leaves thousands of years of prehistory (before the invention of writing) when this could have happened, but it seems much more difficult to design a language without writing, or, for that matter, to do it without the linguistic knowledge that exists today.
Coining of new words has always happened, but that is language change, which develops from an existing language, and not the invention of an entire language from scratch.
You could argue that modern Hebrew is at least partly constructed.
Hebrew fell into disuse and only survived as a 'sacred' language in a religious context. Then, with the rise of the Zionist movement towards the end of the 19th Century, Hebrew was modernised and used as a lingua franca in the Palestine region. In the process, aspects of Hebrew variants were combined, and the vocabulary was extended to allow the use of Hebrew in modern day life.
Cryptolects (aka Cants or Secret languages) come to my mind as candidates. While they are typically not fully constructed, they often contain a constructed core vocabulary making the language unintelligible to outsiders. When they exist long enough, they are learned as first language by the group members.
EDIT: It took me some time of searching for this one because I forgot the name: Eskayan spoken on Bohul island in The Phillipines.
EDIT2: Another example where it is probably no longer decidable whether it is an isolate language or a secret language is the Nihali language in central India.
Depending if you include scripts in the definition of "natural language", Hangul is a famous example of an alphabet that was created in the 15th century and has evolved since then.