There are two separate requirements in WA. One, the operator of a vehicle must have insurance meeting the statutory requirements to operate the vehicle. Two, the operator of a vehicle must show proof of having the statutory insurance when asked by authorized persons. (The statutes have changed recently to allow the operator to show the proof of having insurance by electronic means, such as a smartphone.)
When you were stopped, you could have been issued tickets for either or both of the violations.
In many WA courts, when the operator can show proof of having insurance at the date the police stopped the operator, the court will dismiss the ticket (which is several hundred dollars) with an administrative fee (about $25).
In WA, the ticketed person has only 15 days to choose what to do with the ticket: pay, contest, or mitigate.
You should promptly contact the clerk of the court hearing your ticket to find out the court's procedures for you to show proof of having insurance.
If you do not want to pay anything at all, you need to find a legal reason why the ticket must be dismissed. Hiring an attorney would cost several hundred dollars. If all you have to pay is $25, it may be quicker just to pay. Paying the $25 should have no effect on your insurance.
If you can show proof that you had insurance at the time of the ticket you can get the ticket dismissed. The courts are allowed to charge a $25 fee for the process. Some courts charge the fee and others do not. Many courts will allow you to mail prof to the court, others want you to appear for the hearing and present proof to the judge. You need to contact the court where the ticket is filed to find out what their procedure is. .