Yes, any person can become an American. It is known as assimilation. Basically, it means that the person studies American culture and tries to act more like most Americans. Many immigrants like aspects of American culture and try to emulate them.
People absolutely can transform themselves and become American. We are a country of immigrants and millions upon millions of people have made themselves into Americans. My father is one of them. He was born Filipino but is now as American as anyone.
To become an American, all you have to do (other than the technical details of becoming a citizen) is to subscribe to the core beliefs of American society. You have to come to have a fairly open mind about things like religion, race, and culture. You have to understand that people can be good Americans without being just like you. For my father, that involved to some extent learning to accept the differences in religion given that he came from a country that (especially back then) is overwhelmingly Catholic.
Overall, though, there is nothing that difficult about becoming American. It is done simply by changing ones attitudes about a few things. Anyone can, by doing this, become American.