You don't need wealth to run for the office. Bernie Sanders, while certainly wealthier than average American, doesn't have any more liquid wealth than typical 30-something software engineer, and doesn't seem to be spending any of it on his campaign.
What you need to run is people who will vote for you, and that's a real problem for young candidates.
Bernie Sanders has a job he’s not going to get fired from if he doesn’t show up for months at a time because he’s on the campaign trail.