If i was about to search for another sportsbook using any search engine i would start at youtube / twitch / streaming reviewers about that particular casino.

This way i would get more information regarding trustness, fairness and so on as OP's mentioned.
You could start paying specific streamers for advertising your sportsbook so then your audience could grow and each individual pass that information to another as a chain.

Or you could stream as yourself and explain how users can stand out gambling at your Sportsbook rather than others.

Overall trust comes with time and dedication...