Martin Van Buren, #8, birthed in 1782 in Kinderhook NY, was the first American President not born a British subject nor of British ancestry (Netherlands).
But... the Revolutionary War ended in 1783 actually, so an argument could be made for John Tyler, #10... but he wasn't elected, he took over after William Henry Harrison (#9, born in 1773) died 1 month into office.
That gives us James K Polk, #11, born on November 2, 1795 in a log cabin in Pineville, North Carolina, as the first American President born on undisputed American soil and elected to the office.
Now for the first elected American President born to two American-born parents... :)
Well done!