Seeds don't require a lot of soil for germination. As a matter of fact, I would have lots of problems with your container.

I've always used standard #1020 plastic trays, with drainage holes. I sow two or three hundred seeds in each tray, place them over heat mats, and stick them in my little grow room that we assemble in the garage each winter.

The trays, of course, are very shallow, but the seedlings only remain in them for a very few days after germination after which they are transplanted into trays with plastic inserts.

Since the mix is so low in the box and there is only light from above through a thickish plastic lid don't the seedlings become etiolated?

I keep it simple and use various size flats, pots, or seedling trays, depending on what I'm sowing. I enclose them in a clear plastic bag to retain moisture, place them in the appropriate setting (warmth, light/darkness), and once things start to sprout I remove the bag. :)

I Love it.