How can a person realize that a particular thing doesn't bring "happiness" without personal experience? Buddha was, if I'm not mistaken, a privileged prince with money/health/a social life who realized that none of those things make you “happy” (or even content enough). 

But how can, for example, somebody who has only known poverty all his life attain a true realization that money won’t make him “happy” without firsthand experience?

Or, how is this poor person to realize that money won't make him content when he is constantly bombarded with "evidence" of the opposite, after all, most people with more than their basic needs covered (I mean people of average economy, not the filthy rich) are content enough to not seek a means to end their "suffering".
The core teachings of the Buddha are universally applicable. 


There is suffering. - Everyone knows suffering, rich and poor alike. The suffering of the poor may seem more obvious, but is there any doubt that the wealthy suffer mentally as well, regardless of their resources? 
The cause of our suffering is our attachments. - The wealthy have more to be attached to, in fact. 
There is a way to end suffering. 
The way to end suffering is the practice of the Eightfold Noble Path. 


We really only need to know that we suffer and that we seek relief from our own suffering. But it's a long path. If a person is convinced that money will end his or her suffering, they can give it a go; and then eventually realize that making money didn't end their suffering and pick up where they left off. That sort of thing probably happens a lot. My guess would be that many converts to Buddhism have found the teachings of the Buddha to resonate with them after having first tried other ways of finding happiness. It's because we try other ways of finding happiness first, and learn first hand that the things we thought would bring us happiness, didn't, that we can appreciate the wisdom of the Buddha's teaching.