The EFC isn’t the total colleges will expect you to pay. It’s the minimum. If your child is a US citizen s/he can take the federal student loan ($5500 as a freshman, $6500 as a sophomore, and $7500/year as a junior and senior). I think a $12k EFC is too high to qualify for federal or state grants, but if your child has high stats they may qualify for merit aid.
International students who can’t afford what colleges expect them to pay need to pursue financing in their own country. International.students may qualify for merit too, but if parents can’t pay anything the chances of filling the gap are slim.