The way it USUALLY works is, at the conclusion of the Inauguration ceremony, the new president takes the motorcade to the White House alone and the now-former president is immediately choppered by Marine One one last time directly from the Capitol building to Andrews where he'll next take one last military plane to wherever his new home is going to be - though as Veritable mentioned, they won't be called Marine One and Air Force One at that time. In Trump's case, that would be a plane to Mar-a-Lago, or well the closest airport.
But we already know Trump is not going to attend the Inauguration, and he almost certainly won't receive the Bidens at the White House beforehand either. So he is probably going to take Marine One straight from the White House to Andrews and on to Florida sometime before Biden arrives in the Capitol. If his idea, as has been suggested, is to try and steal press coverage by announcing his 2024 campaign DURING the Inauguration ceremony, he'll probably want to be in Florida already at that time, so he'd probably leave Washington early in the morning in that case.