The Declaration explained why the Thirteen Colonies at war with the Kingdom of Great Britain regarded themselves as thirteen independent sovereign states, no longer under British rule.
Please note that at this time, there did not yet exist a nation called "The United States of America".
Many years would pass before the Constitution was written.
After the war, but before the Constitution, The Articles of Confederation would form a loose grouping of the states also called "The United States of America". Despite the same names, they should be considered two different entities.
Declaration of Independence - July 4, 1776
This is from when the Mexican state of Texas-Coahuila had to deal with impossible problems with Texas's previously promised right to statehood when the Texas area of the state of Texas-Coahuila had sufficient population and infrastructure. The government of México had essentially failed and been replaced. Thus that promised statehood could not be obtained from the acting Government of México. At that time, Texas was still a part of México.
Texas Declaration of Independence