Even with PIE, we can reconstruct that based on its numerous descendants, but with no intermediate forms living or attested in ancient literature, we can't trace its relation to other language groups because there are too many possible sound change permutations to be able to do more than guess about PIE's links to the Semitic or Turkic language groups.
Interesting stuff.
I think I was confused by the term “linear” thinking it was some family of writing. In a very loose way, I guess it is. Looking up the definition I see “linear” seems to refer to a writing composed of simple lines as opposed to a more pictographic form. Although it’s interesting as I remember one of the stumbling blocks to deciphering hieroglyphics is people thought each symbol was a word instead of a sound. So although pictographic looking, the “picture” was only a sound and not a representation of a thing.