No, Alexander Hamilton did not help write the Declaration of Independence.
The Declaration of Independence was primarily authored by Thomas Jefferson in 1776, during the early stages of the American Revolution. While Hamilton played a crucial role in shaping the American government and economy later on, especially through his contributions to the Federalist Papers and as the first Secretary of the Treasury, he was not involved in the drafting of the Declaration.
At the time the Declaration was written, Hamilton was only 21 years old and was serving as an artillery captain in the Continental Army. His major contributions to American political theory and structure came after the Declaration had already been established and the United States was working on creating a functioning government under the Articles of Confederation and later the Constitution.