I concur with @Ned - e.g. Matasovic in "Areal Typology of Proto‐Indo‐European: The Case for Caucasian Connections" mentions trade between Sumerian folks, North Caucasians and Yamana culture. In my humble opinion an important objective of trade was slavery, so even if the trade was indirect through intermediaries, language would have been brought along anyway.
By the way, for gada you might want to take a look at Egyptian "dd" - stability, common Anglicization Djed, also meaning to speak and an insignia; and "mdw" - word, staff (cp. Ger. "Buchstabe"?). Then compare a) "stem" (Ger. "Stamm" - trunk, tribe; also Ger. "Trieb" - ..., sprout); b) "house" - (figuratively) family; c) "Egypt", egy. "hwt (k3 ptah)" - temple (of ptah)" ... So, I suppose the sacrifice made to the mountain gada was to a temple - a stable (permanent) settlement around a pillar (stela - a book staff?). Then consider a current theory for "god" as from a Lombardic "godan", variant of "Odin", a Germanic deity, also "Wotan", which wiktionary gives derived from *weh₂t-. Compare that to "veda" and above "mwt". That's not comprehensive nor coherent, but mighty interesting. Note *weh₂t- is linked to Old English ƿoþ /woːθ/ - sound, noise, cry, '''speech''', articulation, eloquence, song, poetry, voice. But more so Ger. "Wut" - strong emotion; cp. "rush", "rage" with "rushes, reeds" and "papyrus" and the like.