One cannot speak about ethnic and population continuity without uniparental continuity. It is the safest way to detemine regional ethnic/genetic continuity beyond doubt. Because similar ancestral proportions can exist under different scenarios.
For the Greeks, we can say for sure that there was little continuity to moderns from the Bronze Age. However, from the Iron Age we still lack data and even more so from the Roman period, from which we got something more recently, but its still just a glimpse.
Concerning J2a/M410 and ancient Minoan, Mycenaean and pre-Roman Greeks, here are some branches on FTDNA which were found in the ancient Greek DNA record. which could be assigned more downstream:
https://discover.familytreedna.com/y-dna/J-BY759/tree (upstream position of this important branch to get the full context)
Discover more about your paternal ancestry and join in on the research!
discover.familytreedna.com
Discover more about your paternal ancestry and join in on the research!
discover.familytreedna.com
Discover more about your paternal ancestry and join in on the research!
discover.familytreedna.com
Discover more about your paternal ancestry and join in on the research!
discover.familytreedna.com
Discover more about your paternal ancestry and join in on the research!
discover.familytreedna.com
The first thing you notice is that there are barely any big founder events for any of these lineages, especially not in Europe and basically not a single Greek tester.
Therefore, regardless of single Greek testers being found at some point, these branches of J-M410 play no significant role in modern Greeks. Now Greeks are not super well-represented on FTDNA, not doubt about that. But now compare the situation with the big South Dacian founder lineages of E-CTS9320, of which one sample was found in later Iron Age-Roman era Greece as well, plus it has some of THE most important branches of E-V13 in Vlachs in particular (especially E-FT181830) and pretty important ones in Albanians.
It is full of Greek samples, including small to medium sized founder events (like E-FTB51584):
https://discover.familytreedna.com/y-dna/E-CTS9320/tree
Therefore the Daco-Thracian/South Dacian into Vlach and Albanian, but also regional branches from Iron Age to Antiquity, completely top the ancient Minoan/Mycenaean branches of J-M410 we got so far. And that's just a single Daco-Thracian branch, which tops them all.
Here is another branch of the Minoan-Greek sphere under G-P303:
https://discover.familytreedna.com/y-dna/G-Z6147/tree
It has a modern Greek tester, possibly even two (if the Italian is of Greek descent), but still no founder lineage which persisted into moderns with a big significance.
There might be, however, still old Greek branches around, which just happened to not have been tested in the ancients, but so far they are hard to find, to put it that way. Can chance, but so far the regional continuity from the Bronze Age is rather meagre, at least at first glance.