The United States was officially declared independent by the 2nd Continental Congress on July 4, 1776. This independence became a settled fact after the signing of the Treaty of Paris (1783) by the United Kingdom and the United States. However, our current governmental system was not yet in place during either of these times.
For the first 13 years of the United States of America, the government was under the Articles of Confederacy. It created an incredibly weak central government, reserving most powers to the 13 states that were a part of it. The national government had no ability to raise funds directly, and most important matters could be vetoed by a single state. To say it didn't really work is an understatement.