Doesn’t it have to be at noon?
Responsibility, Authority, and Accountability pass in an instant, whether it is a change of administrations, to VPOTUS if POTUS dies, or is removed under the 25th Amendment. There is always a POTUS just as there is always a monarch in Britain. This is why we have Continuity of Government plans and procedures.
The swearing in is a formality. It is necessary, but still a formality.
SpyNavy
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)