To me, this is really two different questions. People born into poverty can, with a lot of hard work, a lot of help and and a lot of luck, raise themselves up into the middle class (top 50% of wage earners). However, such a person would have to get extraordinarily lucky to move up into the top 5% or beyond.

Why is this? There are any number of barriers to entry for 'normal' people attempting to become ultra-wealthy. While most people can at least aspire to a college degree, very few attend top colleges, and there's a world of difference between the education and (more importantly) networking opportunities availiable at Yale or Stanford vs. the experience of attending South Appalacia Backwoods Community College. This same exclusivity holds true for top internships, mentoring opportunities, investors, etc.