Taken in the spirit it was asked, as I take it, I would suggest looking into the Hurrians, who Biblical scholars have associated with the Horites and Hivites mentioned in the Bible. However, there is something quite unique about the Hurrians in that apparently, according to language at least, they were neither Semitic nor Indo-European, yet once occupied a sizeable portion of the ANE and penetrated down into Canaan at one point to settle, which is why the Hivites are mentioned in the list of nations which Israel would have to drive out of the land.
According to the Wikipedia article on the Hurrians:
The Hurrians spoke an ergative, agglutinative language conventionally called Hurrian, which is unrelated to neighbouring Semitic or Indo-European languages, and may have been a language isolate.
The Hurrians also had a presence in the Mittannian Empire. The aforementioned article mentions the following:
Texts in the Hurrian language in cuneiform have been found at Hattusa, Ugarit (Ras Shamra), as well as in one of the longest of the Amarna letters, written by King Tushratta of Mitanni to Pharaoh Amenhotep III.
Edward Lipiński in an article titled "Hurrians and Their Gods in Canaan" in the Polish journal Rocznik Orientalistyczny (2016) mentions:
The first appearance of Hurrians and of personages bearing Indo-Aryan names in citystates of ancient Canaan can be dated to the late 16th century B.C. and be related to the expansive influence of the Mittannian empire.
Hurrian names are attested on tablets that have been discovered in Canaan, such as in Hebron. So that is at least one ancient people group who Israel had contact with from the northern ANE who penetrated southward into the Semitic lands.
As for possible biblical tie-ins aside from the conquest of Canaan it has been suggested that remnants of the Hurrian population continued until the time of King David, as in the article by Aharon Kempinski for Biblical Archaeology Review (1979) titled "Hittites in the Bible: What Does Archaeology Say?", which mentions the following:
The evidence from Jerusalem, however, for the identification of the Jebusites as a Hittite tribe is insufficient. The pre-Davidic population more likely included mainly Hurrian (a population whose origin was in southeastern Anatolia) elements. ...
Remnants of the Hurrian population may have dwelled in ancient Israel up to the time of David. The title for the king of pre-Davidic Jerusalem is ha-Aravna (2 Samuel 24-16). This title has been metathesized (that is, the letters were transposed) from ewri-na, which means “the lord” in Hurrian.
I've seen other articles about the Hurrians in Canaan in the past but that is just a sampling of the information available.