How did Y-haplogroup J2b get to Europe?

Y-haplogroup J2b, defined by the L282 mutation, is found throughout Europe and reaches relatively high frequencies in the southeastern part of the continent. But the question of how and when it got to Europe is still wide open.
It’s certainly native to the Near East, where all of the main subclades of Y-haplogroup J2 show more structure than anywhere else. Indeed, it’s first attested in the ancient DNA record in an Early Neolithic sample from the Zagros Mountains, in what is now western Iran, dating to ~8,000 calBCE.
It doesn’t appear outside of this region until a few thousand years later, when it’s recorded in an Early Bronze Age sample dating to ~2,300 calBCE from a site near the Mediterranean Sea in present-day Jordan.
In Europe, it’s first attested in a Middle Bronze Age sample from the Caucasus Mountains, in what is now southern Russia, dating to ~1900 calBCE. However, this individual’s burial site is practically in the Near East, and, in fact, in terms of ancestry and archeology he is best described as Near Eastern. Importantly, he’s also not directly associated with any population that contributed to the genetic structure of Europeans (for instance, see here).
J2b first appears deep in Europe a little later during the Middle Bronze Age, in several samples from sites near the Mediterranean coast in what are now Croatia and Sardinia. This is obviously nowhere near the Caucasus, but it is in a part of Europe that was linked to the Near East at the time via extensive maritime trade networks. Interestingly, however, all of these individuals are genetically very typical of where and when they lived, in that they don’t show any obvious recent foreign admixture.
So how did Y-haplogroup J2b get to Europe? My view for now is that it mostly arrived with a few sailors from the Near East during the Early to Middle Bronze Age. This is just about the only plausible theory that I can come up with when looking at this map.

The idea that J2b moved deep into Europe along with the population movements of early pastoralists from the Pontic-Caspian steppe seems to be fairly popular online. However, it currently has no support from ancient DNA. In fact, it’s downright contradicted by ancient DNA, because J2b is missing from tens of individuals from a wide range of archeological cultures associated with these population movements. If anyone out there disagrees, then please show me a single instance of J2b in samples from the Khvalynsk, Sredny Stog, Yamnaya, Poltavka, Corded Ware, Bell Beaker, Catacomb, Srubnaya and other closely related ancient European steppe and steppe-derived cultures.
See also…
Ancient island hopping in the western Mediterranean (Fernandes et al. 2019 preprint)
On Maykop ancestry in Yamnaya
Late PIE ground zero now obvious; location of PIE homeland still uncertain, but…

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