Once an individual completes the Oath, he (or she) is President of the United States, under Art. II, s. 1 and the 20th Amendment. The Chief Justice said to Biden: “Congratulations, Mr. President” after the oath was completed. It was before noon at that point. The oath was void.
What you are missing is that even administering the oath of office before noon is a fraudulent and seditious act. According to your logic, Biden could have been sworn in before he EVEN ANNOUNCED he was running for president. Again, once the oath is completed, the oath-taker becomes president. That event occurred while someone else was president. It is void, and it is a usurpation of the Constitution.