As far as I could tell, you have to plant the thorny seed in order to be able to plant a bridge seed.
This is correct, the thorny plants are like fuel which allow you to plant other ones. The idea of the first level is that you see the available oxygen go down when you plant the first two bridges, and then see things unplant when you remove the red plants on the second layer. In hindsight we probably needed a few more tutorials building that up