Before being displaced by Semitic and Indo-European languages, most of the languages of Mesopotamia (e.g. Sumerian), the highland of West Asia (e.g. Elamite, Kassite, Hurrian), Anatolia (Hattic, Urartian, Kaskian), and the Caucasus mountain region (almost all Northwestern, Northeastern and Southern Caucasian languages) were ergative languages, a linguistic feature related to verb tense that is not notable for historic linguistic purposes for being a deep structural grammatical feature of certain languages than it is for the details of how it works when you are using the language.
There are also a few outlier ergative languages that exist today of uncertain provenance. Basque is ergative. A couple of Western Berber languages seem to have an ergative substrate.
I suspect that many pre-IE Aegean languages, including Minoan and a Peloponnese language which is a substrate in Greek share this grammatical trait.
I also suspect that the Harappan language shares this trait (and FWIW, I strongly suspect that the Harappans did not speak a language in the same family as Dravidian with one source of evidence being the nature of the apparent substrate in Vedic Sanskrit - an interesting article on Vedic Indian is here). One clue: "A lot of Indo-Iranian languages are partially ergative as well, with the Kurdish languages, Pashto, and Baloch". This is suggestive of an ergative substrate in the Harappan trade zone which makes sense given that Elamite of West Asia is ergative and that Harappans have trade ties to Sumeria and probably arrives as West Asian farmers from the Fertile Crescent where their agricultural package was developed over Persia to the Indus River Valley. (Notably, there appears to be genetic continuity between early West Asian farmers and modern Iranian Zoroastrians).
It is possible, even likely, that this was also a feature of the language of the early Caucasian Farmers even pre-Uruk.
Kurdish, an Indo-European language spoken in a historically ergative language region, has ergative traits. Related is that: "There is also ergativity in Northeastern Neo-Aramaic dialects, which I’m pretty sure is the only case in the whole Semitic family. Probably the result of Kurdish influence (1,000-2,000 years of diglossia, in some cases)—but possibly a direct holdover from the Iron Age ergative highlands?" Again, substrate or strong areal influences.
I also suspect that there was an early metal age migration from the Caucasus/Armenia region into Anatolia, possibly elite led, that gave rise to the Hattic culture from there, the Minoan culture, that was in place before the rise of the Indo-European Hittites there, which replaced the first wave Neolithic culture of Anatolia that had probably prevailed until then.
It is also possible that this was true even of the early Anatolian farmers although the Anatolian farmer possibility is more of a stretch, but there are plausible alternative sources for ergative languages in Anatolia since then. But, if it was true, then the language of Early European Farmers (LBK and CP) was probably ergative and the possibility of Basque being a language of the first farmers acquired by migrant men in Iberia from their local wives, rather than a transplant from a homeland where an ergative language was spoken. If not, Basque must have been part of a language family that was ergative spoken near where Y-DNA R1b and steppe ancestry were common - a metal working, cow husbandry utilizing civilization that is genetically very much like the proto-Indo-Europeans, but was linguistically very different.
Linguists studying these languages tend to be splitters and not lumpers. But, my own strong intuition is that all of these languages have a common linguistic family relationship, although perhaps at a sufficient time depth that it is difficult to reconstruct a proto-language using the strict comparative method, especially when many of the languages in question are dead and only attested in a fragmentary manner. They have too many features in common and are too distinct, while in close geographic proximity to each other, not to be related.
One plausible means by which this language family may have spread is via the Uruk colonies established in the South and North Caucasus ca. 3500 BCE to 3100 BCE discussed here. It isn't clear when the first farmers reached these areas, but their elaborate phonetics and grammar suggest that these language have had few new language learners or outside influences for many thousands of years. They are relict languages. Razib explains that he is: "alluding to the period between 3500 and 3100 BCE in the Near East when the city of Uruk was the nexus for and a source of a massive cultural and mercantile expansion. I’ll quote Wikipedia:"
Around 3600 BC, during the Middle Uruk period, Uruk trade networks started to expand to other parts of Mesopotamia, and as far as North Caucasus. According to archaeologist Konstantine Pitskhelauri, this expansion started even earlier, at the end of the 5th millennium BC, and continued in the 4th millennium.
Large masses of Uruk migrants settled in the South, and later in the North Caucasus. The sites in this general area include Habuba Kabira in Syria, and Arslantepe in Turkey. Uruk expansion to the northeast included sites like Godin Tepe in Iran. Tepe Gawra, in northwest Iraq, is another important site with deep stratigraphy that includes the Uruk period in later layers. Hamoukar is a large site in northeastern Syria that has been recently excavated; it includes Uruk and pre-Uruk layers.
Uruk enclaves have also been identified at Tell Brak and Nineveh in northern Mesopotamia, and on the Syrian Euphrates at Qrayya, and Jebel Aruda. On the Euphrates in Anatolia, Uruk enclaves were found at Hassek Hoyuk, Samsat, and Tepecik (Elazığ Province, near Keban Dam).
Razib suggests that these were Roman-like colonies of migrants, rather than being integrated with local peoples other than through treaties with local tribal chiefdoms and trade. They vanished as completely as they arose.