I do not believe we truly provide equality of opportunity to all people. I think this is very evident in the United States for the people who want to admit it. Many of our citizens are stuck in low wage, dead end jobs and they have zero opportunity to realistically escape from them.
Right now I do not think we truly provide equality to all people. I do not know if it is something that will ever truly be possible. With companies comes people who think differently than how the rules say and so they may not give someone a job just because they are one way they do not approve of.
Although we promote the idea that everyone in the United States has an equal chance of becoming successful, this is simply not true. Those who are financially affluent have a considerable advantage in the form of being able to afford tuition for private schools and elite colleges, participate in expensive sports and hobbies, and even pay for private lessons or obtain tools and resources that give them a decided advantage over those who do not have the same financial security.
While anyone in the United States certainly has the ability to become successful, some people start off with a higher, better chance than others do. It would be mistaken to assume someone who starts off rich is not at an advantage over someone who starts off poor. They likely will have access to a better education at grade school level, etc., and more of a chance of being able to afford college. And while everyone can get a free public education, some school systems are also better than others. Some children have so much going on at home that they are unable to excel in school. There are many reasons we're not really completely equal in opportunities; there are many factors involved in becoming successful.
No, the United States of America does not provide equality of opportunity to all people. In the United States, white men achieve positions of high authority far more often than any other group. Women and African-Americans in particular lag far behind white men. Thus, as this is the case, the United States does not provide equal opportunity for all.