which event confirmed US independence and set the new nations boundraies?

Answer 1

~There was no single event that did both.
The Treaty of Versailles confirmed the independence of 13 separate and distinct states which allied together under the Articles of Confederation. Under the Articles, there was no single nation.
Boundaries between the new nation states were thereafter disputed for years. Those disputes were contested not only by the states but by the indigenous people living there. The creation of Vermont in 1777 settled some of those disputes, but at that time the creation was of questionable validity because the colonies were still crown territories.

The independence of the USA as an independent nation was confirmed with ratification of the Constitution in March, 1789. The boundaries of the nation were pretty much established at that time. However, the boundaries were pushed from day one, with Vermont being incorporated in 1791 and with claimed national territory being further extended by the Louisiana Purchase in 1803 and by the Treaty of Ghent in 1814 and finally being established in present form in 1959 with the admission of Hawaii.

Answer 2

The Treaty of Paris of 1783, signed on September 3, 1783, and ratified by the Congress of the Confederation on January 14, 1784, formally ended the American Revolutionary War between the Kingdom of Great Britain and the United States of America that had rebelled against their rule starting in 1775.