Tracking for my package says it arrived at OGC today. Any input on whether I wait for them to call me or I call them ? It's Saturday afternoon I'm anxious to go get the serial number for the paperwork first thing Monday visit to HPD.
Sometimes the seller fails to put your name and phone number on the package, and OGC doesn't recognize it as a transfer until they open the box. By then, they might have waited a couple of days to open it after other transfer packages they received.
I see inspection periods usually begin "from" the day of delivery, for example

I believe "from" means "including the day it was received, whereas "after" would be the 3 days following receipt. If you're having scheduling problems, work that issue out with the seller before the window closes.
Since you mentioned getting the serial number for the paperwork, I assume you need to apply for a handgun permit? If so, then go check out the item ASAP if you have an inspection window.
Call OGC and inform them that you need to inspect the firearm by a specific date if that's the case. Work with them to schedule your inspection and get the receipt/specs for the permit app.
Waiting silently for OGC to call could be the worst decision if there's a problem with the firearm.