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The Aeneid by Virgil is not an historical book, but a mythological one, telling a founding myth of Rome. It can be considered to have been written "on commission" by Augustus, to legitimize the Julio-Claudian dynasty as descendants of the founders, heroes, and gods of Rome and Troy (as reported from wikipedia).
There are a lot of different myths about the origin of the founding of Rome, of which Aeneid is just the most famous.
That said, other than myths, the archaeological discoveries told us that ancient Rome was populated by Latin populations, and are Indo-European people, migrated from central Europe around 1000 BC.
It must be taken into consideration that the Italic peninsula was the target of many different migrations, and many different populations were present at the time of the founding of Rome (the Etruscan population was an autochthonous population of central Italy).
So Rome is most likely to have been founded by locals (Latin - Indo-European) people rather than having a Greek origin.
Upvote:7
As far as cultural heritage goes, your best bet is almost always linguistics. The linguistics in this case are quite clear. The Romans were Latins.
Latin is an Indo-European language of the Italic family. This means the cultural ancestors of the Romans were the Italic Tribes who migrated into Italy from the north around 1,800 BC.
The Italics themselves seem to have been part of a group of proto-Indo-Europeans (along with the Germanics and the Gauls) who split off from the rest of the Indo-Europeans as a group in about the 3rd Milenium BCE, likely as part of a joint move into the Danube valley. Those 3 started splitting from each other soon after, with the Germanics moving north and the Italics moving south into the Italian peninsula.
After the Italics moved into the interior of the Peninsula, over many generations they split into various sub-groups, with the Latins being the group that founded the city of Rome. Meanwhile (non-Indo-European) Etruscans became the dominant power in the north, while the burgeoning Greek peoples started colonizing the coastal areas in the south. As you can see from this map below, the Latins were in a rather humble position, and in fact Rome was sending tribute to the Etruscans for a lot of its earliest history.
Eventually of course Rome turned the tables on the Etruscans and became the dominant power in the peninsula (on their way to becoming the dominant power in the Mediterranean world). However, coming up from nobodies wasn't considered a very inspiring story back then, which is why a mythology of descent from a noble people with a very old history (Trojans) became the preferred story.