Wait times vary
It comes down to the lab. If the lab is local it may have a faster turnaround, but the average is 2 weeks. If planned in advance, this can be less than a week, but unless there is CAD CAM milling in office, that is about as fast as one can expect.
In my office we use CEREC to make crowns in a single visit. Since your dentist does not have this technology, it is necessary to take a mold, place a temporary crown, and have a dental lab make the crown. The process usually takes 2-4 weeks. Your dentist should be able to tell you. Anything longer than 4 weeks is too long.