Washington is a shall-issue state, meaning the authorities must issue the permit if the applicant is qualified. Fill out a form, give up your fingerprints, pass a background check, pay $60, and the permit shows up three weeks later.
When I lived in Massachusetts, the drill was, get a drivers license, so that you could get a permit that allowed you to buy firearms. Then, apply for a carry permit, that wasn't really a carry permit at all, as it only allowed you to legally transport your gun between your home or business and the gun club of which you had to already be a member. Provide the cops with a list of current and past employers, current and past roommates, and wait for them to make some calls. Go down to the precinct to discuss the calls. Wait some more. Go down to answer some more questions. Wait some more. Schedule a date at the range for shooting a qualifying score. Take time off from work to shoot the qualifier. After filling out all the forms, answering all the questions, and shooting a decent score, the coppers can issue a permit, unless they don't like the color of your necktie. Total investment, and this was twenty years ago, was four months and over $200.