You could certainly start with 4-6 inches.
When it starts to smell, gets muddy, or flies, add another 4 to 6 inches.
It will vary with climate.
I am in central NJ, my outdoor deep litter never gets below 18 inches.
It is contained by the 1/2 hardware cloth surrounding the run.
My indoor deep bedding, well that is around 6 inches, but very little composting occurs there.