It's actually unlikely that Fort Mountain was built by either the Cherokee or, especially, the Welsh. I've discussed the alleged Welsh discovery of America before, with emphasis on their supposedly connection to the Mandan, but Fort Mountain gets a brief mention as well. The short of it is that the Welsh discovery of the Americas was a convenient historical fiction concocted by 16th Century British historians to justify their entry in the colonization of the Americas. They capitalized on a vague reference in Welsh folklore to the 12th Century prince Madoc emigration from Wales to an unknown destination, and transformed it into a voyage of discovery. Even if Madoc did hypothetically set sail for the Americas, he and his Welsh colonists were at least six centuries too late to build the Fort Mountain enclosure.

The idea that there were a prior wave of Welsh colonists in the Americas clung to the culture of the English-speaking colonists. From time to time, a colonists would describe the local language as sounding like or even being Welsh, despite being Siouan or Iroquoian languages for the most part (the Algonquian and Muscogean languages the make up the bulk of the remainder of eastern languages didn't attract much Welsh speculation). Any legendary people with unusual characteristics would soon be transformed into white Europeans in the minds of colonists. Of particular note here are the "Moon-Eyed People" that often associated with the Fort Mountain Site. This unusual description has led to speculation that 'moon-eyed' refers to the light color of their eyes, which is then used to cast them as having blue eyes and from there to being European. Going back to the Cherokee sources on the "Moon-eyed People," its more likely that the description is intended to mean they were adapted to seeing during the night, as they were also said to be unable to go out in sunlight. They're not Europeans, but one of several other-than-human peoples that were thought to share the Cherokee's world.

The Fort Mountain enclosure fits into a series of hilltop enclosures built Middle and early Late Woodland period (about 2000-1500 years ago, give or take a century). These were important sites in the Hopewell religion that dominated the eastern half of the continent at this time. Fort Mountain area was largely outside the core Hopewell area, but still well within their sphere of influence. It seems the people inhabiting the region at the time picked up a few things, like hilltop enclosures, and gave them their own local flavor - the extensive use of stone, which was used sparingly to the north and west.

At the time, [the ancestors of] the Cherokee were living further north than Georgia, which didn't become part of Cherokee country until their territorial expansion in the 18th Century.