Bought Iphone 13 pro online… when will it arrive?

I bought the iphone 13 pro 512gb graphite as an upgrade to an existing line online 2 days ago directly through verizon. It said “online only” but was not on backorder. Some other 512gbs were on backorder but 512gb graphite showed “online only” and “delivery by October 8th with 2 day shipping”.

Well my order is received but no update on shipping information. My point of question is do you think the graphite 512gb is on a severe backorder until like December because that is what i fear even though the website didn’t say it was on backorder when i bought it. Im just wondering how long i should expect to wait. And I’m upset that in writing it says it should arrive well today.