Not to be read as any sort of judgement, just a look at the envelope from a stamp collector.
That cancel is mostly illegible. But like anything post office around the holidays stuff can and does get messed up.
here's what it should look like.
Depending on when it went in the box, and the pickup schedule of the box, it could have been cancelled later than mailed.
The DV Daniels is a distribution center, located in Kearney.
Most mailboxes have the last pickup at 4:30 or so, a lot in that part of NJ are 4:30 so a letter dropped after that on the 29th wouldn't be picked up until Saturday the 30th.
Sunday, Monday is the 31st, Tuesday the 1st, so the first likely day it got dealt with at the processing center would be the 2nd. If the box wasn't collected - shouldn't happen, but shorthanded on a holiday? Maybe. It would be the same.
Oddly, I can't read that cancel as 02 Jan.
But the 8th or 9th shouldn't be correct either, as the last day for the happy holidays cancel was supposed to be the 5th
https://about.usps.com/holidaynews/postmarks.htm
A bit of a puzzle, If I was looking at the envelope for my collection, I might set it aside as a possible late use of the computer generated cancel.