He was born in the US to the best of my knowledge. According to Citizenship and Immigration Services anyone born on US soil is a US citizen. We can quibble all day regarding jurisdiction but if it goes to court you can guarantee that any person born on US is soil is a citizen at birth and is therefore a natural born citizen. The child has to do nothing. He or she is a citizen with all the attendant rights and privileges. The same if a child is born outside the US to a citizen.
and the courts would be wrong. Why else would the Founders have used a special descriptor for who was eligible to be POTUS and Vice-POTUS?