First thing to do is to pot the seedlings up before they die
If you don't object to it, spray the ground elder where you want to put your beds. Give it a fortnight to kill the roots Make your frames and add any multi purpose compost and dig it into the soil. Add some blood fish and bone fertiliser before planting to get some crops growing this year. Next year you will have your own compost, and you can add some manure in the autumn if you can get it
If you don't want to spray then just dig as much of the roots out as you can, the more thorough the better at this stage, as every bit of root left behind will regrow
Good luck....it takes quite a while to get rid of it entirely though, just hoe it off as fast as you see any regrowth.