Could one make a filter by using fine sand in layers of coffee filters?
Yes, however the can system would be small and take a long time to produce a decent amount of water. You want the layers not to leech over into other layers. Thin cotton cloth or cheesecloth can be cut to work with larger buckets.
But I’d start with a layer of good soil. Then small pea gravel. Then work into finer layers.
Periodically you need to change out the soil layer. Eventually you’ll need to redo all the layers.
If you wanted to make this more antibacterial some people make a layer of silver coins in between a couple fine sand layers.