“We are one family, race, kindred, all here in the pursuit of happiness.” Gov. William Seward, 28 Sep, 1860
How could the Founders maintain same kindred citizens and immigrants? Article 1 Section 8. “Uniform rule of naturalization”.
bushpilot2 quoting Jay: "...Providence has been pleased to give this one connected country for one united people -- a people descended from the same ancestors, speaking the same language, professing the same religion, attached to the same principles of government..."
Clearly, both quotes are a matter of political hyperbole, not biological or historical fact.
Europe in Jay's time as well as Seward's included many different nations, religions & denominations, spoke many languages and sent disparate peoples to settle the New World.
Of nations & languages we could easily name England, Scotland, Ireland, Holland, Germany, Switzerland, France, Italy, Sweden, Spain, western Asia & Africa.
Of religions & denominations: Christians, Jews, Protestants, Roman Catholics, Anglicans, Presbyterians, Lutherans, Congregationalists, Quakers, Mennonites & Moravians.
As for principles of government, certainly by 1800 all were committed to the US Constitution though even by then great "factions" formed around differences of opinion in how it should be interpreted.
So your quotes have nothing to do with biological or historical reality and everything to do with the political necessity for transcendently unifying hyperbole.
They should be understood as metaphors intended most likely to raise the spirits of disheartened electorates.
Today we say in that same spirit: "One nation, under God, indivisible with liberty & justice for all."
You disagree?