In this fascinating article from the BPS Research Digest, a study is described where university students were asked to rate several character traits of a person after seeing their photo for just 100 milliseconds.
"The ratings they gave the faces correlated strongly with ratings given by other students who were allowed as long as they wanted to rate the faces. The strongest correlation was for trustworthiness. 'Maybe as soon as a face is there, you know whether to trust it,' the researchers surmised."
"These findings suggest that minimal exposure to faces is sufficient for people to form trait impressions, and that additional exposure time can simply boost confidence in these impressions. That is, additional encounters with a person may only serve to justify quick, initial, on-line judgments," the researchers said.
What does this mean for you as a speaker? Just that the minute you walk into the room, your audience members are already forming judgments about you. It's important to remember that, from the moment you get out of your car or walk out of your hotel room, you are "on."
I can't tell you how to look more trustworthy. If you're not a trustworthy person, I guess the audience will determine that right away. But I can tell you to be aware that judgments are formed in an instant and that the more professional, approachable, positive and easy to work with you are, the better impression you're going to make on organizers and audiences.