Are you an expert in the field. Most reliable sources consider Latvian and Lithuanian to be Slavic (includes Balto-Slavic--the most encompassing definition of the term).
It's got a gazillion conjugations and declensions ~ and tracking each one of them back to the closest source language(s) would probably pin it down as a creole with no purely Slavic roots.
Still, some of those roots can probably also be found in the ancient background of one or more of the modern Slavic languages. This is something that would lead to the confusion that Lett is Slavic, or even derived, in part from Slavic linguistic input (beyond modern words of course).
Sometimes the development of a creole takes a different track, and like English, the conjugations and declensions are dropped. Sometimes the replacement (for purposes of grammar) may be word order or just a lot of mind-numbing agglutination.
My understanding is that Lett has neither ~ and that leaves it out of the Uralic/Altaic or Fenno/Scandian orbits. (BTW, this question of Lett being as old as Sanskrit has been around for ages. Even the Nazi ethnologists used to debate it. That's before they lost WWII and we killed them off).
It's possible that ancient slave routes passed through this part of the Baltic, and that's what led to the creation of a regional trade language made up of so many pieces from so many other Indo-European langauges. Unfortunately they appear not to have written any histories until the coming of the Swedes and Greeks.