Some mosses can grow in full sun but it depends on the species. Mosses are usually not very good competitors so you find them in areas poorly suited for vascular plants, like areas of low fertility, extreme pH, dry for part of the year, etc. In areas where other plants can grow you would need to remove the competing vegetation in order for moss to thrive or manipulate the growing conditions. It can be a challenge to figure out how to get a particular moss to thrive, but you can always start small and repeat whatever seems to work the best.