It may be a little more diffcult to do so these days, and "hard work" certainly doesn't guarantee anything, but of course it is possible, and lots of people do it.
Just looking around my small circle of friends and family:
My wife is a professor at one of the most prestigious private universities in the south, makes six figures - and grew up in trailers in Florida with a single mom. That's pretty poor. While I wouldn't say she is "rich" she certainly would have been if she had stayed in industry, where she was fast-tracking to the executive suite (academics is her second career, because she got bored with industry).
One of my good friends, who is a professor at USC in L.A. grew up a poor Korean immigrant (his parents immigrated here when he was a little kid), and his parents worked their fingers to the bone to give him a good life. He's also making six figures, and his house (that he bought for 300K six years ago) is now worth about a million.