I have not been able to find much information specific to the 'office'. The title 'president elect' has been used for decades, but it seems to be an unofficial term. If it is an unofficial term, when did it start being used?
I have been able to find information about the Presidential Transition Act of 1963, but it does not have info about an official office for the president elect (that I know of).
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What you're asking is basically the equivalent of "Why is Jello powder in a box labeled 'Jello' when it's clearly not Jello yet?" President-elect is not an office per se, but it is a necessary (and officially recognized, as in the Presidential Transition Act of 1963) state of being in the process of making a new President. You can't just say some magic words over Jello powder and have it instantly become Jello, there's a preparation stage. Likewise, the oath of office doesn't instantly confer all the knowledge necessary to start being President on Day 1 in office, they need to learn what they'll be facing on Day 1 ahead of time.