People become believable when they stop pretending every answer is immediately available.

Someone who has an immediate answer to everything is either extraordinarily well informed or not tracking the difference between knowing and speaking. Most people conclude the second. Saying that you will need to check makes everything else you say more solid, because it shows there is a standard being applied. Willingness to not know is part of appearing to know.

Next time you are asked something outside what you actually know, say you will find out rather than constructing something plausible. Then find out and come back. Both halves of that are what build the impression.