Here is a secret; building departments are usually much easier on homeowners than they are on builders and architects. You do not have to be a contractor or an architect to get a building permit in many places. You can pull an “owner-builder” permit. You can update the permit after it's issued to add your contractor.
The first step is to understand the local permit process and plan requirements. The best way to do this is to call your local building department and talk with them. In the most restrictive towns and cities, you will need zoning and architectural review, soils and engineering reports and more. But in much of the country, it is still a pretty simple process.
Once you have all of the documents required by your local building department, try submitting them in person. I like to go when things are quiet (not first thing, at the end of the day or just before or after lunch). If you treat the plan checkers like the experts that they are, and take their advice, they can be surprisingly un-bureaucratic.
And here is a bit of advice that you really should follow. If an unlicensed and/or uninsured contractor tells you to pull an owner-builder permit find a different contractor.