New Employee - Insurance Delay

I just started with the state in the second week of last month. I’m working in a regional office for State Parks in SoCal. I submitted my insurance paperwork on my second day to the analyst who has been handling all my onboarding and coordination with HR. I was expecting my health insurance to kick in this month, but didn’t hear anything. We reached out to HR and they said that SCO hasn’t sent my info to PERS yet so they weren’t able to enroll me in any benefits. They said they had reached out again to SCO to get the ball rolling last Tuesday but I haven’t heard anything since.

How long could this take? I’m starting to run low on medications I use daily and don’t want to have to resort to opting in to the expensive COBRA policy from my previous job if I don’t have to.