Purifying water without filters that have to be cleaned and replaced, typically involves evaporating the water and then re-condensing it to produce clean, distilled water. We want to do this efficiently, and using afordable, widely available materials.
The simplest way to purify water, no matter how dirty, is to boil it, collect the steam, let the steam cool, collect the condensation water. What you get is pure, distilled water. This water is free of contaminants UNLESS the original, dirty water contained another liquid with a lower boiling temperature lower than the boiling temperature of water, for example, gasoline or alcohol. Microbes, viruses, dirt, heavy metals all get left behind when you distill water. Like everything in life, distilling has advantage and disadvantages. Distilling purifies almost any dirty water, but consumes a lot of energy in part because you heat the whole pot of water, including the left overs.
We can reduce the energy needed by spreading out the water and by heating only a little bit at a time. 1) Spread out a cloth in the bottom of a shallow, water proof box tilted at a 30 degree angle. 2) Pour dirty water into the cloth slowly. Let the cloth become soaked. Let excess water drip out the bottom of the box. 3) Warm the air entering the bottom of the box with pretty much any heat source. 4) Capture the warmed, moistened air leaving the top of the box. 5) Capture the water in the moistened air as it cools and condenses. This is again, distilled air. The advantages of this are: 1) lower temperatures will work because we are not boiling the water, just evaporating it. 2) we do not have to heat a pot, but just the air passing over the wet cloth. The disadvantages are: 1) the manual effort of slowly pouring water into the top. 2) the cloth will get dirty and thus, less effective.
We can keep the cloth clean by getting the cloth wet using wicking action instead of pouring dirty water onto the cloth.
Everyone Everywhere can purify water using: cotton cloth for evaporation and for wicking; any water proof material (plastic, metal, wood, clay, glass, whatever is available and affordable); warmth from any heat source (engine exhaust, fire (wood, grass, candle, dung, leaves, etc.), sun light, etc.
Large volumes would mean commercially produced equipment.