Hixkaryana is a Carib language, spoken by some 500 people, in the states Amazonas and Pará in Brazil. I am interested in the history of this language, but very little is known. Can someone help me to find out when this language came into existence?
Languages don't technically just "come into existence" as they're products of language evolution that is quite subtle, gradual and slow. Language is not only defined by mutual intelligibility - or lack of it - with other languages, but also by its speakers' concept of a separate linguistic identity.
I don't think you could get a precise date, but as Manjusri stated your best bet would be glottochronology or diachronics as to determine the amount of separation between Hixkaryana and other Cariban languages. I can't recommend sources of whose content I can be certain as Carib languages are quite far from what I know well, but you should research what you can on the history of Cariban languages, Proto-Cariban and most of all this new work published by Spike Gildea in 2012 ("Linguistic studies in the Cariban family") if you're serious about it as it seems interesting.