No, Alexander Hamilton did not sign the Declaration of Independence.
Although Hamilton was a key figure in the founding of the United States and played a significant role in the American Revolutionary War, he was not present when the Declaration was adopted in 1776. At that time, Hamilton was still a young man and serving as an artillery captain in the Continental Army. His political influence and contributions came later, particularly through his work as the first Secretary of the Treasury and his involvement in the drafting of the Federalist Papers.
While he was a strong advocate for independence, his formal political career began after the Declaration was signed. Thus, even though Hamilton is often associated with the early foundations of the U.S. government, he is not one of the signers of this pivotal document.