Make the sign for eat by taking your dominant hand, forming a flat ASL letter O sign, and tapping your fingers to your mouth once. To sign food, make the same handshape but tap your fingers to your mouth twice. This universal sign for eating is the same sign used for food. The only difference is that verbs are signed once, and nouns are signed twice.
Eat is one of the most common first signs. Make the sign whenever you offer food to your baby, when they eat, and just after they have finished. Your baby will be highly motivated to learn this sign, as they will quickly learn that using it enables them to get food whenever they are hungry. As your baby gets more advanced, start introducing the names of specific food items, so along with the general word eat, your baby can start using more specific words like jam, or blueberry.
Eating is one of our favorite signing opportunities. We sign food, we sign more, and we sign all done as part of our meal repertoire.