The Homeric epics and Virgil's Aeneid, the telling of the myth of Rome supposedly founded by the descendants of Troy, are, well, myth. The Iliad tells us more about the culture of Archaic Greece at the time that the epic was put in writing than it does about the mythical time of Greek Gods and Heroes that is narrated in the epic. Same with the Aeneid, which is more about Rome and the way Rome saw itself than it about the actual historical origins of the Romans.

This said, is there evidence that could theoretically link the Latins of the time of the founding and early days of Rome with the Greek world? Let's look at a couple of objects from the archaeological record, the Corinthian Chigi Vase and the Laconian Arkesilas Cup.

The Chigi Vase is an "olpe", a wine jug that in Archaic Greece could have been used to serve wine to aristocrats getting together for a "symposion", the custom of elite men getting together to drink wine and enjoy dance, music and poetry. The Chigi vase was made in Corinth, and its protocorinthian style allows us to date its manufacture to about the year 650 BCE. It famously depicts a battle between hoplite forces, but it also includes images of young men hunting lions and riding horses, and of children hunting rabbits with dogs. Seen as an overall narrative, it tells how to become proper Greek heroic men through the stages of youth to the adulthood as warriors. The imagery is very much a product of Greek culture of its era. And yet, it was excavated in Veio, an Etruscan city that was just north of Rome. How did it end up there? It is unlikely that it was brought to Etruria from Greece by someone hoping to find a buyer for such an unique, high-end artifact used in the Greek symposion and depicting Greek culture. It is more likely that it was commissioned by someone from Etruria who was familiar with Greek culture and customs of that time.

The Arkesilas Cup is a xylik, a vessel used by the Greek elite for drinking wine at a symposion. It is from Laconia (Sparta), and can be dated to about a century later than the Chigi vase. It depicts a very Greek imagery, the loading of agricultural cargo in the Laconian colony of Cyrene, in North Africa. Again, like the Chigi vase, the Arkesilas Cup is very much a product of Archaic Greek culture and elite customs. And yet it was excavated in Etruria, in Vulci, about 100 km north-west of Rome.

Taken together, these two objects tell us that the culture and customs of Archaic Greece were known and sought after in the area surrounding Rome, in a period ranging from the middle of the seventh century to the middle of the sixth century. There is no reason to think that this would have started suddenly in the year 650, so it is likely that there was commercial and cultural contact between the Etruscans and various parts of the Greek world in the early seventh century and possibly mid to late eight century. These are the years that are traditionally given for the founding of Rome (753 BCE) and the time of the seven kings of Rome. So while the founding myth of Rome in the time of Heroes and Gods, is just a myth that is designed to connect the history of the city to the great epics of the Greek world, it is not completely impossible that there was some actual human or cultural Greek DNA in the very early days of Rome, passed through them by the elite Etruscans.

Sources

Hurwit, Jeffrey M. "Reading the Chigi Vase." Hesperia: The Journal of the American School of Classical Studies at Athens 71, no. 1 (2002)

Osborne, Robin. Archaic and Classical Greek Art, Oxford: Oxford University Press