It's been my experience that cultures of trust build when groups create explicit shared agreements on how it works together. The significance of this effort is that the scope of a group's creativity is equal to the scope of its trust and that groups move at the speed of trust.
The process I use has three elements:
Defining common principles
The group identifies everything that matters to people as they think about how they work together. This usually includes principles related to communication, organization, governance and courtesies.
Crafting proposed agreements
The group works together to craft proposed agreements in how things could work for everyone, given the group's realities. The key is that they are very realistic, respectful and relevant to the group's performance indicators.
The group tests and critiques proposed agreements. They then tweak or implement what was tested based on how they worked in real contexts. They do with as many principles as they consider significant to the culture of trust in the group. New group members are onboarded to existing agreements and included in the development and improvement of next agreements.
Fundamental to the nature of trust in groups is that it cannot be commanded, incentivized or trained. A culture of trust grows through the development of authetic agreements.