Each day in between missions, use the mirror table to start a general mission with each character. Take mental notes of which ones you use as there is no checklist in the game.
At Research Level 15; you can research a schematic for the WAR ROOM that allows you to re-roll one of the three maps for the day, for a chance to get a different character as a general mission leader. Keep persevering if you don’t get the character you need, you’ll get them as a mission leader eventually.