If a baby passes out, how can I make sure they are still breathing while unconscious?

ABC. If baby is unconcious conduct quick evaluation: check the airway , check for breathing by looking at chest and abdominal wall movements and listenning with your ear to baby's nostrills and mouth and possibly feeling flow of the air on your ear/cheek also skin would turn pale or cyanotic if not breathing, and finaly check heart rate. Recomend to take basic life support training with such concerns.
Chest movement. Look for chest movement from breathing, or place a mirror near your baby's nostrils to see if it fogs from your baby's breath.