Since "Credibility" and "Trust" are largely synonymous, let’s just call it “Trust.”
Establishing trust is not a one-way street. It is almost impossible to do it unless the feeling is mutual.
Trust is the most important buying decision factor for most prospects, when they are making significant buying decisions. We should also include Respect, which is the 2nd most important buying decision factor.
All of the ideas that have been posted here are good ones. On the other hand, if they really did work, most salespeople would be using them because they are easy to do. And, since trust is the most important buying decision factor, all that use those ideas would be highly successful.
So, what is missing?
It is that trust and respect are largely Emotional reactions rather than Intellectual decisions - especially when there is no history between the parties. Thus, in order to be highly successful, salespeople need to utilize an emotional process designed to achieve Trust and Respect with new prospects. Furthermore, that process must develop a Relationship of Mutual Trust and Respect in order to be highly effective.
For those that want to know more about how to influence prospects (or anyone) at the level of their emotions, often called “intuition,” I suggest reading “Power vs. Force” by Dr. David Hawkins.