For what its worth, I think if you added some good soil/compost mix to give more depth to the soil, it will work. Bring the level up to within two or three inches of the top.
Does it have adequate drainage? That is an important consideration also.
It's actually just sitting on the ground there. I haven't added the soil yet. There is no bottom to it, so I guess to answer your questions is that there's a lot of depth and a lot of drainage? ... unless I'm missing something.
So I plan to move it somewhere - haven't decided where yet, but the floor will just be the earth - and fill it up with purchased garden soil like you say. (I do have compost going, but it's a new garden and not there yet).
Do you reckon that will work?