You mean like the Supreme Court in a unanimous decision, written by Chief Justice Waite:
At common law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives or natural-born citizens, as distinguished from aliens or foreigners.
Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
-Minor v Happersett (1879)
There’s no mention there of what happens when a child who parents are either both American citizens, or one is, happens to be born on foreign soil, or even on the frontiers of America that weren’t states.
Also no mention of what happens when parent is a natural-born American citizen and one isn’t.
And I see it says anyone born on American soil is possibly a natural-born American citizen, regardless of their parents’ status.
Chester A. Arthur, Republican President
Chester Alan Arthur was born October 5, 1829, in Fairfield, Vermont.[a][5] Arthur’s mother, Malvina Stone, was born in Vermont, the daughter of George Washington Stone and Judith Stevens. Malvina’s family was primarily of English descent, and her grandfather, Uriah Stone, fought in the Continental Army during the American Revolution.[5] His father, William Arthur, was born in Dreen, Cullybackey, County Antrim in what is now Northern Ireland; he graduated from college in Belfast and emigrated to Canada in 1819 or 1820. Arthur’s mother met his father while William Arthur was teaching at a school in Dunham, Quebec, just over the border from her native Vermont. The two married in Dunham on April 12, 1821, soon after meeting.[5] After their first child, Regina, was born, the Arthurs moved to Vermont. They quickly moved from Burlington to Jericho, and finally to Waterville, as William received positions teaching at different schools.[5] William Arthur also spent a brief time working to join the legal profession. While still in Waterville, William departed from his legal studies, as well as his Presbyterian upbringing, to join the Free Will Baptists, spending the rest of his life as a minister in that sect.[5] William became an outspoken abolitionist, which often made him unpopular with members of his congregations and contributed to the family’s frequent moves.[6] In 1828, the family moved again, to Fairfield, where Chester Alan Arthur was born the following year; he was the fifth of nine children.[7][8] He was named “Chester” after Chester Abell, the physician and family friend who assisted in his birth, and “Alan” for his paternal grandfather.[b] The family remained in Fairfield until 1832, when William’s profession took them on the road again, to several towns in Vermont and upstate New York. The family finally settled in the Schenectady, New York, area.[9]
The family’s frequent moves later spawned accusations that Chester Arthur was not a native-born citizen of the United States. When Arthur was nominated for vice president in 1880, a New York attorney and political opponent, Arthur P. Hinman, initially speculated that Arthur was born in Ireland and did not come to the United States until he was fourteen years old. Had that been true, opponents might have argued that Arthur was constitutionally ineligible for the vice presidency under the United States Constitution’s natural-born citizen clause.[10][c][11] When Hinman’s original story did not take root, he spread a new rumor that Arthur was born in Canada. This claim, too, failed to gain credence.[11]
https://en.wikipedia.org/wiki/Chester_A._Arthur
Was there ever any evidence presented that Arthur’s father ever became an American citizen? He certainly wasn’t a natural-born one, either way. So “natural-born” already here didn’t mean the child of two “natural-born” parents.