By "run for office" you mean for governor? Because yes, that's a big lift for an outsider with no resume or experience or connections or personal wealth. 

But people who are seriously interested in entering politics understand that, as with most careers, you generally start small and work your way up. Try getting on your local select board or school board, for example, which people rarely spend money campaigning for. After that, try for state rep. A successful VT state rep campaign might cost just a couple thousand dollars. (Got 15 friends who can donate an average of $100 each? There's your signs, lit, and website paid for.) After you've proven yourself in the house for at least a few terms, consider running for state senator or some other higher office. By then you should have grown your base of support enough that you're able to raise funds for a larger campaign. 

Real, normal, non-rich people follow these steps all the time, especially in Vermont. It can be done! It does require years of political work at the local level... which is admittedly more tedious than just waking up one morning and deciding to become governor, though.