Justice Thomas recommended the Donofrio case for conference on Dec 5 (10 days before the electoral college meets to cast its votes). Four of the 9 justices at the private conference must vote in favor of further proceedings. One assumes a quick, emergency hearing should four agree.
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.