In the modern world, we idealised the ancient Greeks and Romans, even though they were actually a terrible time to be alive, but we look on them with rose coloured glasses.
Who were the ancient Greeks / Romans for Ancient Greece and Ancient Rome? Who did they look back on with rose coloured glasses?
They must have had people that they thought were older than them in terms of civilization. They couldn't have known that almost all of modern Europe bases their civilization on what was to them their contemporary time. So they wouldn't have known that they were the "first", who did they think were the first, for them?
More can be said if anyone wishes to add something, but in the meantime here are a few older answers you may enjoy: