As a 'thumb-rule' 6" is what I would call minimum. You may be able to skirt around that by choosing varieties that have shorted roots (i.e. Little finger carrots) You will have to monitor water closely as summer temps will dry out that shallow soil quicker.

What summer crops were you planning?

Personally, I built my raised beds 12". I just felt the extra depth would benefit things like tomatoes, squash, etc. Never regretted it, although it is extra work and expense. Rosemarino, since you lined your bed with plastic, is drainage going to be an issue?

Well, I belong to a "backyard growers association" in my town and lining the beds with plastic is recommended because of the lead content that you can basically assume is in your soil. I could have the soil tested, but have not.
I am actually pregnant right now, and hauling all that compost the other day to make the bed was SO hard that I was hoping that I would not have to do any more! But I agree, more is advisable.
I am planning on planting whatever will grow in a less sunny location. The only spot I had was near a tree. So when it leafs out more, I'll be able to see if I should just stick with lettuces. Of course, I was hoping for tomatoes, beans, eggplant and peppers! But likely those will need to go in pots on the patio...

Just bought a book about SFG but did not see what the depth to plant tomato plants is. My SFG is 46" x 46" x 5.5". Should I purchase another garden to go on top of the one I have? Any advice? Have not set it up yet so still need to get peat moss, vermiculite and mixed compost.

I have a ground hog problem now. Is this garden doomed?