The OP asked a “what if,” question. This means we assume the situation in the post is correct whether or not valid. It could apply to Mr Obama or anyone else holding the office.
As others said the first option is impeachment. Would this work? Most likely, no one likes to be conned, especially the voters. If you could show a president, elected to office didn’t meet the qualifications, it’s hard to justify NOT to impeach him
If any Congressman didn’t they’d likely face a HUGE backlash at the next re-election. If any Senator didn’t vote for removal same thing.
OK step two would arrive if congress refused to impeach or remove the president who didn’t meet minimal qualificaitons.
In this case it would be the Supreme Court. This would result in several things.
The court would rule the person bringing suit has no standing to bring suit, thus skirting the issue.
The court would rule it’s poltical and again skirt the issue.
Or the court would hear the case.
So now we’re on the third step, the Supreme Court could rule that since he was duly elected that he can stay. That would end it. Remember the US Constitution isn’t what IT says, it’s what the Supreme Court says it is.
For instance, the Supreme Court once rule they government has no right to regulate child labor. There was even an amendment that never got ratified to try to overturn that choice. Of course today, government at every level regulates child labor? Why, because the US Constitution is what the Supreme Court says it is.
Another instance is when the Supreme Court (Dred Scott case), said that no black person, regardless of free/slave status could be a citizen. They passed the 13th amendment to overrule the case.
On to the next step, the Supreme Court could say, “No the president did not meet qualifications and therefore isn’t president.”
This would result in the most serious problem. The Supreme Court can make any ruling but as Andrew Jackson said, “The Surpeme Court made the decison, now let them enforce it.”
In this case the Vice President would be president and we could have dual governments.
At this stage it’s a free for all for discussion with anything from a civil war with one half the nation supporting the unqualified president verus the vice president, to anything
When people ask these question, it’s just for fun.
To answer Mr Obama proved he was qualified isn’t an answer. It isn’t what the OP asked. A type of question like this is just fun to talk about, whether it’s Mr Obama or anyone else, but it’s really a debate or opinion.