No, airbnb founders did not believe. In fact, Mark Zuckerberg did not believe either. Nor did Larry page.
They got there by learning from user, questioning their "belief" and iterating.
Nate: '... so I at this point decided to move to Boston. Had other priorities in my life. And pace suddenly slowed down .... Have you told Michael that I am working on other things?'. https://www.youtube.com/watch?v=Ya0I6oz7q9U&fea...
Mark: '.. well, it does not have to be anything more than a college friend website. That is a great product.' https://youtu.be/aQ5otpv6kTw?t=252
Larry page: ... tried multiple times to license their technology and later sell the company for a few millions and later for a few billions. The gap in their asking price and market offer kept them going.