James K Polk, born after the Revolution, born in SW Territory.
Pretty sure Andrew Jackson was, too, but I need to check.
According to wikihahahahahahapedia, Andy Jackson was born in the Carolinas in 1767 ... IOW, not just prior to the Constitution, but prior to Independence. He qualified under “citizen at the time of adoption”.
Andrew Jackson was born in 1767 and took part in the American Revolution. James K. Polk was born in 1795 in North Carolina. He later lived in Tennessee but was not born there. (Tennessee became a state in 1796.)
Jackson was born a British subject. Polk was born in NC.