Note that even when colleges do meet “full need”, that scholarship does not always include things such as travel, health insurance, books, spending money, etc. which can run into thousands of dollars. Understand what a “full scholarship” means at each school and be sure your family can manage any other costs.
If your family can pay the application fees, it is fine to give it a shot and apply to some US colleges that appear to be affordable – but you should look at affordable college options elsewhere as well.