“or—according to the law at the time-—a father who was American by the time of one’s birth”
The law at what time? Certainly not after the passage of the 14th amendment, which is the only place in the Constitution to define citizenship.
The law at the time of birth of the individual in question.
The 14th Amendment required states to recognize former slaves as citizens.
This case is not about whether anyone is a citizen. It is about the definition of “natural born citizen,” which is not answered by the 14th Amendment (although that amendment may illuminate the answer).