Coolidge was sworn in by their own father (who was a notary public).
Having found this form in the Constitution, I had it set up on the typewriter, and the oath was administered by my father in his capacity as a notary public, an office he had held for a great many years.
(Coolidge, Calvin, The Autobiography of Calvin Coolidge (1929); Sann, Paul, The Lawless Decade (1957). Cited from here)
Finding a qualified Notary Public in Washington, DC doesn't seem like an insurmountable obstacle even on short notice.
As such, all you need to swear in a new President legally is somone who can take an Oath from them, SCOTUS isn't needed.
If it takes longer than 5 minutes, I'd be surprised (You need to say the Oath of Office, then say you're resigning).
So theoretically, if everyone cooperates, you can go through not only Biden, but 288 different chain of command Presidents in a day.