I think that what you're looking for is Manifest Destiny, the idea that it was natural, required and proper of the settlers to expand across the continent.
Some connected this to God (that is, that God devised this expansion as His plan), but God is not always necessarily connected to this idea.
In the 19th century, there was widespread belief and conviction in the US that immigrants were predestined by the destiny of settling a whole North American continent to spread democracy and capitalism, as well as that the USA were predestined from God. Thus, in 1845, the phrase "manifest destiny" was coined, which expressed the philosophy that led to the territorial expansion of USA in the 19th century.
