The Romans indeed had an idea of ‘primitive’ man existing prior to agriculture, but their basic concept would be fairly alien to us.
Their idea can be traced back to ancient Greek poets like Hesiod. In Works and Days Hesiod said that in very ancient times the earliest people were a ‘golden race of mortal man.’ This has since been called the Golden Age of Man. These people knew no sorrow and did not have to work for their food because ‘the fruitful earth unforced bare them fruit abundantly and without stint.’ They lived in peace, happiness and leisure.
Next came ‘a second generation which was of silver and less noble by far.’ These people did not live in the same paradise as those in the Golden Age. They had some sorrow and troubles, but it still wasn’t that bad of a life.
After the Silver Age came successive ages of bronze, heroic and iron. Hesiod lived in the Age of Iron, and ‘men never rest from labour and sorrow by day, and from perishing by night; and the gods shall lay sore trouble upon them.’
You might notice that things are getting progressively worse over time, with the exception of the Heroic Age, which coincided with the ancient Homeric tales of heroes and demigods. This idea of devolution is in contrast to our modern ideas of primitive life and progress.
Moreover, the people are behaving worse over time, not just suffering from a less bountiful land. The earliest people were sinless, but by the age of iron people were dishonouring their parents, telling lies, going to war and doing all sorts of evil things. So there is a bit of moralising going on here.
This basic idea of a golden primitive age was very compelling and it has lasted even till today in some forms. A related artistic strain was the pastoral, where the primitive shepherd lived in happy harmony with nature. Many writers touched upon this in ancient times, like Ovid, Virgil and Theocritus. This later merged with ideas of the Garden of Eden to produce the idea of a beautiful, fruitful and primitive place which was populated by simple, happy and virtuous people.