I assume that this question refers to “global understanding” within the United States as it does not seem likely that people in India or China, for example, have much of a need to understand Hispanic or African American culture.
Within the United States, it will be difficult to force people to understand minority cultures. There is a great deal of resistance to the idea of minority cultures as many people feel that minorities should simply assimilate into “mainstream” American culture. In essence, it may be possible to give other Americans the chance to be exposed to Hispanic or African American culture, but it will not be possible to ensure that they make the most of these opportunities.
Perhaps the only way to ensure that everyone would be exposed to such cultures is to teach about them in schools. Schools could have social studies units about these cultures (which will be difficult since there is no single Hispanic or African American culture). They could require students to read works by authors from these cultures or listen to music of these cultures. This would encourage students to understand the cultures. However, it would be no guarantee. There are plenty of things that students are exposed to in school which they do not end up understanding or caring about. It is likely that these cultures would end up in that category for many students.
Thus, it is not going to be possible to guarantee that all Americans will come to “understand” these cultures, but education can at least give them the chance to do so.