I’m just transitioning into 3* rosters. I wanted to know, if I sell my 1* characters, will I still be able to participate in the first node of DDQ? Or will I be locked out?
No, you need at least one 1* character to do it.
So you keep Juggernaut, or Iron Man if you don’t have the first one and it will be widely enough to finish it. 
Perfect. Thank you.