How large is your aviary? Is it for button quail exclusively?
You can use concrete for an aviary base. In fact, it is my favorite flooring type. It is easy to clean and disinfect, as well as being highly predator resistant. You can also do concrete as the base layer for protection and then cover with sand or another bedding for comfort. I highly recommend all outdoor aviaries have a solid floor or layer of underwire to deter digging predators. Hard dirt or gravel is not enough. Many nocturnal animals would love to get inside a button quail aviary.
I've never tried sand, so I cannot say how easy it is to keep clean. I have heard mixed reported from people who use sand in chicken runs. Some love sand. Others consider it a messy waste of time. I think it would be impossible to really clean it without replacing it ... but the quail would love the free dust baths.
For my aviary, I have a base floor of concrete pavers and then I put down paper for easy clean-up. I use 4ft wide rolls of heavy paper used for floor protection during construction projects. It is easy to work with and rolls out quickly to cover a large surface area.
My adult button quail have no issues with the paper, but I'm not sure about newly hatched babies. The one time I had baby button quail, they ended up in a brooder because the mother wasn't keeping them warm, so it wasn't an issue. I've used a few brands of paper, some are rough and others are pretty smooth. If the paper is too slick you could lay down some other bedding on top for better grip when babies are expected. Paper towels or even a thin layer of sand or shavings should do the trick, I would think.
Depending on the size and style of aviary, you could also use some form of loose bedding such as wood shavings or pellets. Like paper (or sand) it does need to be replaced on a regular basis. It is messier than paper and lighter than sand. Kind of in between those two flooring types, with pros and cons from either side. Wood shavings are my go-to choice for chicken coops, but I like paper better for an aviary.
Another factor to consider is moisture - is the aviary fully covered? Most of the floor coveringsI have discussed do not play well with water. You will want to keep paper, and shavings as dry as possible for best effect. Concrete, gravel, and wire can get wet. Sand is best when kept dry, but as long as you have adequate drainage, it will survive getting wet.