What is the connection between the stated goals of the constitution and the purposes of government?

The stated natural established "goals" would be the "How" Through the established system of government.

(ex: how are we going to bring order and protect the future of their security.)

The purpose of the government due to the Deceleration of Independence, established, laying down a foundation of principles, laws, order brought & organizing its power in such form.

The connection would be the "Do ordain" (order) through we the people.