Legal Question in Criminal Law in Washington

You can but not yet. The rules related to restoring the right to a firearm parallel those related to vacating a conviction. You'll need to wait until you've completed the term of supervision, get a discharge and then behalf for a couple of more years. Look for some of the answers related to vacating a conviction for the specifics.

At your service,

You become eligible to petition for restoration of gun rights on the 5th anniversary of your conviction or release from custody (whichever is later), PROVIDED you have no new convictions.

Although you will need a certificate of discharge to be clear under federal law, it is unrelated to removing a firearm disability under state law. If you have fulfilled all of the obligations of your sentence, including satisfaction of legal financial obligations, you are entitled to a certificate of discharge. DOC is obligated to file a discharge if everything is completed by the end of your supervision; however, if you had any remaining obligations when supervision was terminated, e.g. owed money, then it is your obligation to file for a discharge.

Vacating a conviction is neither required nor necessary; it is unrelated and has no effect on gun rights.

Clarification - If you have a prior class B felony, your waiting period to restore gun rights is 10 years.