The good news is flat feet is normal in babies and children and will usually develop into fully functional feet overtime. In fact, the extra fat in the midfoot of small children is protective! Reducing impact on the still-developing bones. Kids don't usually develop a visible arch until around age 6 or 7, after the extra fat has disappeared.
And even then you don't need to rush in with arch support if they still have flat feet. As long as your child has no diagnosed musculoskeletal issues and is developing normally it's best to let them use their feet so their muscles and tissues can strengthen naturally.
Bernie Landels' book Finding Their Feet is a great place to learn all about a child's developing foot.