One day before your move-in, call City of Seattle at 206-684-3000.
Give them your new address and your unit number.
Give them your name and tell them you want to open a new account
Give them the day of your move-in.
If you have had an account with them before, you will be all done.
If not they will tell you that after you are done setting up account on the phone
You will need to go to their office, 4534 University Way NE, and show ID.
You can do it as soon as you get off phone or the next day.