The forgery of a selective service registration is a crime and would have to be investigated and prosecuted in the criminal justice system. IANAL, but I don't believe a private citizen could bring an action based on the SS registration forgery or the LFBC forgery for that matter.
AFTER conviction of forgery of the BC or SS registration, then grounds for numerous eligibility actions would be established, but I believe that Congress would have to investigate and impeach a sitting president, or objections to electors casting votes for him would have to be made if conclusive proof of forgeries could be established even before a conviction in the slow-moving courts.
I want to see the court case challenging the eligibility of the voters who voted for Obama
They could of course plead insanity