This does seem a little early.
Usually they've done it towards the end of December.
If the aim is to give an incoming Senator "seniority," all it takes is for the outgoing Senator to resign a day or an hour or a minute before the new Senate convenes on January 3rd; that does give the new Senator "seniority" over all the others coming in.
The shortest Senate term I'm aware of was, interestingly, the first woman to serve in the U.S. Senate, Rebecca Felton (D-Georgia) in 1921 or 1922. She served three hours, and then the later-famous Walter George (D-Georgia) took it over.
Three hours was perhaps enough for her, a retired schoolteacher, because she was 92 or 94 years old at the time.