Some of the indo-european languages* are documented to be up to 3800 years old, like Hethitic, or 3600 years for Greek. So one would expect that the others are not substantially younger. (* I refer to the proto languages that followed proto IE, like proto Germanic, proto Celtic and so on.)
Now there seems to be a hypothesis that proto Germanic could be as "young" as only 2500 years, which is based on some "facts" concerning the dating of Grimm's law. As far as I found out myself so far, it deals with:
- a few names in latin texts (like Vahalis for the river Waal), but those are questionable because Latin had no letters for fricatives.
- a few names in Germanic (like welsh from the celtic tribe of the Volcae), but there are no clues when those entered the germanic vocabulary.
- the "hemp-hypothesis" (Barber 1991) that germanic *hanapiz was not inherited from proto indo-european but instead is a loanword from Cimmerian from the mid 1st millenium BC. But this hypothesis violates Occam's razor and raises several questions.
I'd like to dig deeper into those things, maybe someone can point me to the right publications.