OK, I'm not sure I follow your connection. How does that say anything about what a natural born citizen is? It says they are writing a Constitution for themselves and their children - but it doesn't say "only our children and ourselves". In fact, the Constitution explicitly states how we can add more people to Ourselves corporately!
That's right. When you add to Ourselves via naturalization, you are adding to We the People. Once you are of the People, your Posterity are natural born People, too.
The Preamble says that the Constitution was established to secure the liberty of the People and their Posterity. That does not exclude foreigners from coming to the United States, nor from living here among the People. But, foreigners are NOT We the People, and their posterity was not meant to be secured in the same way that We the People's Posterity was being secured.
You can argue that foreigners enjoy the protections of the Bill of Rights just like We the People, and I'd say that you are right.
However, foreigners do NOT enjoy the rights in Article I or Article II, in that they do NOT get to vote for Representatives in Congress or for Electors for the President.
Therefore, securing liberty to Ourselves and our Posterity also refers to granting voting rights to citizens only. Again, the posterity of citizens is what is referenced in the Preamble, or the citizen children of citizen parents.
-PJ