Is there any scientific evidence that a firmament may have once encircled the globe?
Short answer: No.
The word 'encircled' is probably anachronistic, since the ancients who spoke of the 'fimament' typically thought that the Earth was flat, and imagined the sky above it as a dome. If there was any circularity associated with that model, it's associated with the idea that the flat Earth might be disk-shaped.
Or if it is physically possible that such a thing could of existed?
The Earth was never a flat disk, so no. I suppose that it's physically possible that a roughly spherical planet could be surrounded by a shell of some sort. But suggesting that at one time in history the Earth was surrounded by such a shell that no longer exists is nothing but sci-fi imagination.
Now, by firmament, I am using an interpatation of the passage in genesis referring to God creating the firmament and separating the waters from the waters.
Ancient cosmogonic mythology is fascinating. These stories kind of represent the first stirrings of philosophy. But it's foolish in my opinion to try to interpret these stories as if they recorded historical facts.
It could refer to a layer of water surrounding the upper atmosphere, or possibly just a ring of ice surrounding the planet.
In ancient Mesopotamian mythology, the idea of 'the waters' symbolized primordial chaos.
Water was the primary engine of chaos in early Sumerian and Akkadian society, since floods periodically devastated their early cities. Even the rain tended to dissolve their stuctures, which were typically built from sun-dried unfired dirt bricks.
More philosophically, water was seen as being without form. Water takes the shape of any container that it's in and has no innate shape of its own. So in ancient Mesopotamia, creation was imagined as an act of taming the primordial waters, creating dry land and a world of stability. Form was imposed on shapelessness.
That's what the 'waters above and below' stuff is basically talking about. The universe was imagined as inherently chaotic and formless, and the Earth was conceived as having been created by the earliest gods through a process of separating the waters and creating a dry bubble of stable reality in between.
This, btw, is what the 'flood' myth was about. The threat that the ancient Mesopotamians always felt that rational form and stability might disappear and chaos return.
The Hebrew writers of Genesis were just making allusions to middle-eastern cosmogonic mythology that was already several thousand years old by the time they wrote, retelling the traditional story in such a way that their god Yahweh played the central role.