In the beginning, there was a creator deity who resided inside a deep chasm splitting the mountain we see throughout the game. This deity created souls (glowing symbols) and spread them throughout the world. From these souls, birds and plants (flora and fauna) were born, as well as the sentient Armless Biped species, tentatively dubbed "the Ancients". The Ancients worshiped their creator, who appeared to them as a source of blinding light and ultimately gave them the "red cloth"—a pseudo-living construct serving as a source of (nigh) infinite energy. Using the red cloth to power their machinery, the Ancients reached the pinnacle of their civilization, but the red cloth ran out and a civil war broke out over the last remaining pieces. The War Machines/Guardians were developed (probably out of cloth "whales") to help the war effort, while the native flora and fauna were completely exterminated, turning the land into a barren desert populated only by the remaining scraps of red cloth. The Ancients as a species likewise didn't survive the war, and their souls dispersed into the ether once again.
The origin of the white cloth
The white cloth was developed by the Ancients to wear in extremely cold environments, such as the mountaintop where normal red cloth quickly runs out of energy while the White Robe doesn't. As such, the depictions of the Ancients wearing white robes before being given the red cloth are probably anachronisms.
Probably not: the White Robe does lose energy and get frozen too, it just replenishes itself by touching the ground. You still have trouble flying in some places if you don't have a partner to keep you warm (and even then).
Fact is, the White Robe is much more energy-efficient in harsh environments than the Red Robe, so the basic cornerstone of the theory still stands.
The Traveler is the personified lament of the Ancients
The vision at the Temple indicates that the Traveler is a being condensed from the spirits of the Ancients, that returned to the ether after the war. Throughout the game, the Traveler witnesses the rise and fall of the Ancients' civilization but is unable to alter anything that's happened and eventually returns to the beginning of the road to relive it again. Combine it with the fact that the Traveler is probably not the same species as the Ancients (who are much larger both in the visions and on the glyphs), and it's a likely guess that the Traveler is an artificial being called into existence by the extinct Ancients to lament their self-destruction.
Everything in the game is made of the same substance
Contrary to the previous theory, not only are the Travelers and the Ancients different stages of the same species, but so is every single creature, and also sand, light, everything — it's all made from the same glowy dust you see the air shine with around you as you walk into the light at the very end of the game. This comes from an observation in the pink desert chapter: if you approach the crumbled tower (on the right, just before the buildings at the end of the level) fast enough and look up carefully, you will see two comets launch from the mountaintop, but one falls and collides with the ground... exploding into a Glowing Symbol, a trail of glowing symbols dust (akin to what you fill the Temple level with), and a bunch of small fish-papers.
So if Journeyers turn into comets and comets are made of glowing symbols and fish-papers come from comets, and dried large banners/flags sometimes dissolve into smaller papers...
You often see symbols glowing in the air during history lessons cutscenes: at the beginning of the first one, plants and what looks like birds appear in the same way as fish-papers/dolphin-carpets and white Travelers/Ancients; and at the end of the Fifth Confluence cutscene, you see a red Traveler being born apparently from air or stardust, while symbols are glowing in the air again.
Every living creature is made up from those symbols you find.
What's more —though it might be simply an artistic choice— the sand that covers the ruins at that last moment appears by shining. Sand itself might also simply be dust from the same substance; this explains why it shines so much in some lighting. Plus, if we deduce that 'flying energy' is produced on contact between travelers and paper-creatures because they're made of the same base substance, since sand is stone ground into dust, this can explain why White Cloaks regain energy from touching the ground (which is always either sand, rock, stone buildings, or snow — I'll get back to snow later). White Cloaks are simply the next stages of the same species as Red Cloaks and thus have the ability to store more energy and regain energy from more sources, but at the root it's because sand and stone are still that same substance.
In the Temple, you fill the room with some sort of gooey water/light particles/liquid aether, which gives you energy as well. It seems to be the thing the Ancients powered their machines and cities with — the white light you see in the buildings during cutscenes. What did they produce it with? As far as I can tell from cutscenes and glyphs: from red scarf paper.
In the Paradise/Apotheosis level, that substance is back but indistinguishable from water. The water itself, from the waterfalls, gives you energy as well, and it glows faintly. At the very end, it's simply LIGHT that gives you energy, and for a few long seconds, your character itself turns into light. That light seems to become snow (which is just another state of water) at the mountaintop, or is it the snow that produces those shining symbols floating in the air?
You can go even further — the sounds you produce give energy, the sound wave and halo/bubble of light that reach other creatures. Symbols emit sound! Sound reverberates differently throught the aether! Your light/sound waves make sand scatter, light up blank walls and extinguished lanterns, warm up frozen creatures and Travelers. Touching each other makes Travelers not only replenish energy, but glow red, keep their voice, and stay warm, while cold gusts diminish that energy.
All that being said, I'm still unclear what the first, fundamental state of it is: is it light, sound, warmth, air, aether, symbol particle? Is there a linear evolution from first to last spanning every single possible stage, or different branches of species: light/sound, water, sand, cloth creatures, and the Ancient Lines? Are cloth creatures Travelers-in-the-making, or distant cousins?
But the more I think about it, the more I'm convinced that everything in the game is made from that same raw material which gives life and flight.
Additional notes: it's pretty clear to me that War Machines (which are made of stone, emit light, and steal your energy upon contact) are powered by the papers or carpets they contain (which is why you have to free some in the pink desert), and possibly themselves power something in the towers at the end of the pink desert level.
Also, I mentioned plants: the Flower and the flOw creature both also react to your touch and make the same kind of sound. The flower shines with small light dust-particles, and the creature is apparently made of pure light and -as far as I know- can appear in at least two different places but only in the glowy aether-like substance you fill the Temple with, never in normal air.