I would cut through the cardboard when you plant your transplants. Because the bed is so new and the material won't have had a chance to break down yet, the plants will need a little dirt.

I think you'll want to add some more material to your bed, either now or as you collect it. The material will break down and you'll be surprised at how little there is. I filled a new 15" bed in the fall. I heaped it about as high as was practical and held it in place over the winter with some landscape fabric stapled to the top of the bed. In the spring, I added some more to the top. It's now 4-6" below the top of the bed. The beds I built last year did the same thing. I added to them in the fall and they are 4-6" below the top again. I think I will always have to add to them but the worms love it!

Here is a link that might be useful: Tales of a Transplanted Gardener

Greenbeen, thank you for the advice. I will poke the holes then under each plant as I plant them. You are right about adding to the box; this box, which is 4x4 took 15 bucketfulls of stuff, and I can see it needs about that much more. My crystal ball sees a lot of exercise for me in the future....;)

I not an expert at planting in a new bed but I agree with yuliana that you need to add a lot more material. It's surprising how much it condenses but then so does a compost pile. I was very happy with the beds which overwintered and were then planted to vegetables. I double-checked the book about planting perennials and bulbs in a brand new bed. She said she anchored the base of perennials with upside down sod and put bulbs in the very bottom on top of the paper. I decided it was too risky to leave perennials and new shrubs without much soil so I have put them in the beds, banked with the same soil I would use if I were planting directly in the ground. I'm working on two beds. One is already full of lasagna material so I push some aside, place the new plants and surround with fresh soil and compost. The other bed is going to end up with pockets of lasagna material to be ready next year and right now has islands of shrubs and a few perennials all banked with soil.

When adding, look for some higher nitrogen additions (a.k.a "greens") to balance out the "browns" that compose most of it now. The initial setup of a lasagna bed is a SFG related subject where a bit of reading on the composting forum can help quite a bit.