What claim does jefferson make in the first paragraph of the declaration of independence, and how does he say he will support that claim?

As history changes, and people/nations evolve, it becomes necessary for them to be independent of any other country/power on which they relied. They feel the need to break those connections that bound them, and to finally emerge as a country of its own, a country which doesn't need to count on others in order to thrive and prosper. God has given everyone equal rights, and thus no country has more rights than any other. This newly founded country will become respectable through its own effort, and not through the help/or the dominion of another country. The Americans felt impelled to separate from their mother country, Britain, and eventually create a dream of their own. 
All men are equal - God has given them those unalienable right