Americans believe in their mythology. In other words, we really believe in the right to life, liberty and the pursuit of happiness. We are independent, but caring. We will reach out to help those in need, either in our own country or in others. We also value democracy, capitalism and justice.
To me, the only thing that you need in order to be a true American is a basic commitment to the ideas of democracy and tolerance. Beyond that, you do not need to have any particular experiences.
To be a true American, you have to believe that democracy is the best possible way of government. You have to believe in limited government (as opposed to unlimited, tyrannical government). You have to believe in a general level of toleration. By that, I mean that you have to accept that people who are not like you in terms of race, religion, or political ideology can, nonetheless, be good people and good Americans.
Without these ideas, I do not think you can be a good American because these ideas form the basis of our society and our system of government.