Here’s how this has worked in the past (I’ve been through this >10 times with iPhone orders):
First of all, do not order your Verizon iPhone from Verizon. Order it from Apple. You will be asked to input your information to Verizon from there (e.g., identifying information, whether you’re keeping an existing phone number, etc.). Do that, so your iPhone will arrive ready to be configured on Verizon’s network.
Assuming you complete your order before the iPhone 12 Pro runs out of stock, your order will ship, likely from China, likely roughly Sunday (Oct. 18) such that you will receive it on Oct. 23. A signature will be required when delivery occurs. You will be told the date to expect delivery at order time.
You may go to Apple’s website (or the Apple Store app) today and choose “Get Ready” under iPhone 12 Pro to prepare for some of the steps.