Hi Alie.
As Bob has said the majority of small turned boxes would be made with the grain in the spindle mode.
It is not hard to hollow end grain, but there is a technique to it. What they call back cutting.
You need a spindle gouge sharpened into a "lady's fingernail" shape, You then partially shape the outside of the box mounted in your chuck. Then cut a shallow 'V' into the center of the blank, and useing the gouge as a push drill, bore down the center to the depth you wish the box to be.
Then position your gouge with the flute pointing to approx 10 o'clock the tip just in the lip of the hole and scoop out towards your left shoulder taking light but positive cuts. Basically using the lower side wing to cut with. You continue in this fashion until you have the basic shape you are looking for, then use a scraper to shear cut around the inside to remove any tool marks. Sand and finish!
Nowt to it, BUT you do NEED practice to use this method! Good luck.