I am over 30 days for paperwork needed but the offices are closed. Are there drop boxes at local offices? Specifically Kent and Puyallup WA.

Yes in side

I helped my friend get a first social security card recently at Kent location and the process was to call in, schedule an appointment, then go to office for appointment. It was a relatively smooth process for us and she received card in less than ten days from time of appointment. Just be patient on phone as it takes a bit of time on hold before you talk to a person for appointment.