It isn’t timely until after the Electoral College votes, and Obama becomes President elect. Until then, the 20th Amendment doesn’t apply. There is no Constitutional authority to knock him out of the office until he is President elect. None.
If he committed fraud to gain the Dim nomination, then he theoretically could be impeached, but that would only be operative after he becomes President. Fat chance Pelosi would allow it in the coming session of Congress.
So, the time for the USSC to rule is between Dec 15 and Jan 20. That’s the window. Before 12/15 and it’s not timely. After Jan 20th and the Court has no authority over the matter of qualification.
If the SCOTUS decides on 12/5 to take up the matter, they could simply require Obama to produce an authentic birth certificate by a date certain. It would then be available within the window of which you write.
Frankly, I don’t see getting the 4 votes necessary, but all 9 justices, regardless of political persuasion, should have an interest in whether the winner of the general election for President of the United states has the basic qualifications to serve.
All Obama has to do is produce an authentic birth certificate, not COLB, and the matter is closed, assuming he was borh in HI.