Trust is built in the boring weeks
Nobody trusts a manager because of a speech. They trust the manager who did what they said during the forty weeks when nothing was on fire. What that looks like in practice.
A new manager I was coaching asked me how to get his team to trust him faster. He had been in the role for six weeks and could feel the distance. People were polite, they answered his questions, and they told him nothing.
I did not have a shortcut for him, because there is not one. What I had was a list of small things that had worked for me, none of which are impressive on their own.
Do the thing you said
The first deposit is the smallest. In a 1:1 someone mentions that the build has been flaky and it is costing them an hour a day. You say you will look into it. What happens next is the whole relationship.
If you look into it that week, come back with what you found, and either fix it or explain why you cannot, that person now has evidence. If you forget, they also have evidence. Most managers I have watched lose a team did not lose it in a big moment. They lost it one forgotten follow up at a time.
I keep every commitment I make in a 1:1 in the same document I keep the notes in, with a checkbox. Before each meeting I read the open ones. It is embarrassing how much of my reputation with a team comes down to a checklist, but it does.
Tell them the thing you are not supposed to tell them
There is a category of information managers hoard by default: what leadership is worried about, why the reorganization is being discussed, what the real reason for the deadline is. The instinct is to protect the team from noise.
My experience is that the team hears the noise anyway, in a worse form, and the only thing my silence protects is my own comfort. So I default to sharing, with the boundaries stated plainly. "Leadership is nervous about the Q3 number. That is why the pressure on this project just went up. I do not know yet what happens if we miss it, and I will tell you when I do."
The first time you do this, people look at you strangely. The third time, they start telling you things in return.
Take the blame in public and the credit in private
When a project I owned slipped, I stood up in the leadership meeting and said it slipped because I underestimated the integration work. I did not say the engineer who did the estimate got it wrong, even though he did, because I approved it.
He heard about that meeting within a day. Nothing I could have said to him directly would have done as much.
The reverse matters just as much. When the same project landed, I sent the note to leadership with his name on the design and hers on the migration, and I said in the note that I had mostly gotten out of the way. That was true, and they both saw it.
Be the same person on a bad day
Teams calibrate on the worst version of you, not the average. If you are calm for eleven weeks and then snap at someone during an incident, the snap is what they remember, and every future incident carries the question of whether it will happen again.
I am not naturally calm under pressure. What I do is buy myself time. During an incident I say less than I want to, I write more than I say, and when I feel the edge coming I hand the next question to someone else. It is a technique, not a personality, and the team does not need to know the difference.
What trust bought me during the AI rollout
The year we moved to an AI first way of working, trust was the thing that made the difference between a rollout and a mandate. The engineers who were skeptical told me they were skeptical, in detail, because they believed I would not hold it against them. Two of them became the best critics of the program and, later, its best advocates. On a team where people had learned to keep their doubts to themselves, that skepticism would have gone underground and the adoption number would have stalled with everyone smiling.
I did not earn that in the rollout. I earned it in the boring weeks before, one closed checkbox at a time.