BBB is a waste of time.

First, call AS and explain the situation. If it's not resolved to your satisfaction file a DOT complaint. The fact that the airline doesn't offer first class is irrelevant; the customer is not expected to know that. The airline advertising something for sale that doesn't exist is a DOT violation; and while AS will likely ignore a BBB complaint, they are required to respond to a DOT complaint, and if the response is that first class doesn't exist but they are offering it for sale anyway, the DOT is not going to like that.

The fact that the class of service sold doesn't exist is actually a point in your favor; that should be the main point in the DOT complaint.