For Goddess of Democracy, you draw your hand of Event cards. After checking them, the eligible player immediately discards one non-Scoring card, and draws a replacement for it. Then the Communist player proceeds with his first card play.
Thanks for your answers!
My mistake was that I assumed the discard and draw replacement would take place at the very start of the turn before the draw of the complete hand. At this moment the player couldn't have a scoring card.
The online rules are very clear on that (4.5.1) but I've read over without recognizing it.