There's no trust or belief - you're just trading one scarce in demand resource due another scarce in demand resource - nothing more and nothing less.
This is the reason your money becomes worth less when we print more. A vendor selling whatever will want even more because his product is just as scarce as it was before, but what you're trading for it has become less scarce, and so has less value.
And taken to extremes this value can approach 0 quite rapidly. Trust, belief and all these things don't matter if you're trying to trade me something I see as less valuable than what you want in exchange for it.
You walk into a store, pick up a box of eggs, bonk your rock on another rock, the other rock makes a happy beep or turns green, and you walk out.
There's no scarcity or demand or anything going on besides "everyone with the rocks trusts the rocks"
We're all going to pretend to trust the rocks as long as we can, because the alternative is violent chaos.