Trust between two people resembles a protocol negotiation more than a personality trait. Each party makes a small offer, the other party responds, and the relationship advances one round at a time. Skip a round and the connection downgrades or fails.
Trust at scale — across teams, across organisations — works the same way, just with more parties and slower round trips. The handshake is the whole game.
Run the handshake on purpose. The system you build with the people who completed it is the system that ships.