I think the beginning of this video explains best Starting new galactic war and i don't see any cards. Explore new planet and it offers me to discard the new card... By default there should be 3 slots empty at start. Sometimes it works that i go back to menu and reopen the save, to see cards appear but not always.
I had this issue too. In my 5 galactic war plays on absurd, I lost 3 without a win, and the very first one was not my fault because it was "no slots" start. I argue I got bull tech the other ones too, one time I got 7 techs and 0 extra slots so just a ton of wastage.