This Dan Ebbert’s Expression for Position (on each layer)will do the trick:
minX = 0;
maxX = thisComp.width;
minY = 0;
maxY = thisComp.height;
minZ = 0;
maxZ = 1000;
seedRandom(index,true);
random([minX,minY,minZ],[maxX,maxY,maxZ])
Change the numbers as needed, like the 1000 pixels for Z depth.
You can add the expression to a lot of layers quickly by first adding the expression to one layer (Alt-Click the stopwatch, then paste in the expression), then select the expression, Edit>Copy Expression Only, then finally select all the layers to get the expression and Paste.
Note: the arrangement changes everytime you add a layers, so when you get close to having as many layers as you want up there, and if you like the pattern, stop. If you need to, you can add small Solids as layers (also with the expression) until you find that pattern you like, then you can go back and turn off the eyeball for the extra layers (the solids).