The causes of poverty are hotly debated in our society.
Liberals would tend to argue that poverty is largely caused by a lack of opportunity. They would say that poor people have lower-quality schools and therefore lower life chances. They would say that a lack of good jobs for those with poor schooling is also a cause of poverty.
Conservatives would look more at the culture of the poor. They would argue that things like lack of individual responsibility and bad behaviors like having children out of wedlock are to blame for poverty. These explanations do not focus on lack of opportunity.
We cannot know which of these views is correct, so there is no way to say objectively if poverty is caused solely by a lack of opportunity or if that is just one factor that can contribute to it.
The former answer makes some good points. I would add three more perspectives that argue in favor of the idea that there are limited opportunities to certain segments of society.
First, it is a pretty clear there are limited opportunity for the poor from an educational point of view. We can see this in the educational system. If you go to a private school and compare it with a public school, there really is no contest in practically all areas - teachers, facilities, after school programs, to name a few. From this perspective, there are certainly less opportunities in poor public schools. Some public schools are great, but they are usually in areas of wealth.
Second, when we consider the parental connections, everything becomes amplified. Richer people have legacies in universities, the ability to get tutors and whatever else is needed, not to mention professional networking that helps tremendously. In many ways it really is about who you know.
Third, there are also more subtle benefits for people who are in the richer segments of society. They can talk the talk and walk the walk of their peers. There is a sense of ease and belonging. People in education call this social capital. These intangibles do make a very important difference.
Finally, is it possible for people with little to make it? Of course, they will have to work harder or get a lucky break.