North Country Blue Devils goaltender makes a big save in the 2013 12U B State Tournament

Buy a set of goalie equipment for each mite team and have the players rotate so everyone has the opportunity to try out playing goalie.
Incorporate goalies into practice at all levels. At beginning levels, you can set aside one station during each ADM style practice to focus on developing goalie skills and drills. Focusing on hand-eye coordination, getting up and down quickly and certain skating techniques are transferrable to all hockey positions.
Educate parents and players. There is often a stigma surrounding goalies some of which has to do with cost of participations and pressure. Providing them with goalie highlight reels, stats on how much more ice time goalies see, etc. can help overcome their doubts.