Answer:
I don't think sand filling is as sturdy as gravel filling
you may be thinking of getting it done quickly but quickly may have a price to pay in the long run.
2nd Answer:
The reason to use sand under a slab on grade is so that it can be leveled more precisely than can gravel. If the fill is not perfectly flat, it can "reflect" cracks up through the slab, later.
The use of compacted crushed rock under the sand is completely dependant on the type of soils at the site. Crushed rock may be desirable with some soils to "bridge" over soft areas, or with other soils to create a layer to drain water out from under the slab.
Many locations call for 6" of compacted crushed rock overlaid with 1-1/2" - 2" of sand.
The "quickest" backfill is pea gravel, but it must be constrained at the outer perimeter so it cannot migrate away from under the slab.