When you start a new job, you are in a temporary state of incompetence. No one expects you to have all the answers and to know everything; in fact, people will be suspicious if you imply that you do.
Avoid the temptation to think you have to be the savior and have immediate answers. You will generate goodwill and support by reaching out to others, listening, trying to be helpful, and committing to showing others that you were the right choice for the job.
Establishing your credibility takes a variety of skills, primarily: having a sound strategic agenda, being on top of the details of the business, listening and learning from your boss or other executives, communicating clearly, building a strong and committed team, and maintaining a certain amount of humility.
While you’re going about asking questions, listening and learning, the most important thing you need to determine - besides all the basics like what your job is, what your superiors expect of you, and how to actually do your job - is how to make a real impact. You can take some time with this so don’t rush it.
But before long, it’s a good idea to remind people that you’re not just there to ask questions and listen, and that the management's original reasons for hiring you were valid. That you are actually capable of producing results. The way you do that is to set a goal and plan to accomplish something reasonably visible and impactful.
In the management book “You’re In Charge – Now What?” by James Citrin and Thomas Neff, the authors recommend you to consider such fundamental questions as: What do you hope I do? What are you concerned I might do? What are you concerned I might not do?