For the development of the western European tradition, you might be interested in these earlier answers of mine:

• Before 1700, were there any books or plays set in the future? What were their predictions about what it would be like?
• What did people in the Middle Ages think about the distant future?

Previous to Augustine, who lived from 354 AD to 430 AD, the predominate view of history was that it was cyclical. They believed that the world would cycle through ages. So they would probably recognize the height of the Roman Empire as a "golden age" but there would inevitably be a time of decay.

Augustine introduced the idea that time moved in a linear fashion, as in his mind time was essentially unfolding according to God's plan. Christians at the time believed the return of Christ was imminent, so their view of the future was apocalypse and salvation for the believers. Previous to Augustine, most people's view of the future would just be that the past would be repeated.

Source: Medieval Worlds An Introduction to European History by Jo Ann Cruz and Richard Gerberding

Edit: Made Augustine's dates a little more specific

Followup, would Lucian's Vera Historia (not sure what the Greek would be) be considered a sort of future prediction or scifi, even though it is satirical, or is it purely fantasy? I was reminded of it when reading the post, but I don't quite know how to categorise it.

You might consider taking this question to r/askliterarystudies because they might have texts or notions that aren't listed here.

I also want to add that although you probably aren't thinking of religious prophesy, religion so dominated the daily lives of most civilizations, and so religious prophesy is a form of imagined alternative futures. You could argue that the Book of Revelation (in the Bible) is a prime example of an albeit freaky imagined future, even if it was religious.