Trustworthiness is being believable before proof has to be produced.

The value of being trusted shows up in the gap before evidence arrives. Someone says something and people act on it, because the record suggests it will hold up. That saves enormous time and it is earned entirely in advance, through a long history of statements that turned out to be accurate. You cannot build it in the moment you need it.

Be careful with claims you cannot back, especially minor ones where nobody is checking. The habit of accuracy in small things is what pays out when something important is on the line and there is no time to verify.