In testing supernova I of course tried building ships asap. This seems to be a bit tricksy in my hands. My first ships didn't show up in the ship building list; they did later so I suspected perhaps a turn had to go by before they showed up. Today I went further and picked up the battle cruiser tech, then tried to build a new ship medium sized. I could not get the game to take my new ship and I pondered that maybe I didn't have some prereq tech. But if the hull type shows up in the building list, it should be buidable no? Huge likelihood that I am just doing something wrong.
Doing some more testing I will try to be more specific.