In my opinion, trust is indeed something you earn. You can not command trust ("you have to trust me!"). So your point of save environment I fully endorse.
The most important one for me is to really give trust yourself, and put yourself in a vulnerable position, open yourself in order to stimulate openness from someone else
If team members experience this, then there is a possibility that trust grows. This is depending on the mindset: "what is in it for me?"
Clear, consistent, transparent vision, mission, strategy and goals are also propelling trust.