You said it yourself – building trust between your characters is instrumental for what you want to happen. So let’s look at how trust is built in relationships.
1. Communication. No relationship grows without healthy, two-sided communication. So give your characters opportunities to talk to one another. If they’re not naturally chatty, force them into situations where they’ll need to or want to speak to one another.
2. Trust is based on history – not on short-term decisions. To that end, as your characters begin to develop relationships with each other, be sure that they begin to consider the consequences of their actions in the long term, and not just in the short term (unless their character dictates otherwise).
3. Be sure your characters are honoring their commitments to one another, both large and small. If someone says to another character, “I’ll keep you safe,” be sure they show that they’re helping to keep that character safe in some way.
4. Ensure that your characters are showing one another respect. Even if they don’t have respect for one another at first, this is something that can grow over time. Gimli and Legolas don’t respect each other’s mutual races at first, but getting to know one another allows them to gain a respect for each other’s heritage despite their initial heritages in LoTR.
Above all, remember that relationships are a constant work in progress. So as you’re building your plot, remember to also be building your relationships. You may even build a chart for each relationship that coincides with the plot, and scribble in notes that help you figure out what should happen with each relationship so you can be sure to write in certain details and moments to help with the development of their relationships as you go along. Ultimately, it’s all about remembering to let the relationships constantly grow, along with the characters.