What day was the declaration of independence submitted?

There is no exact date. In fact, it is not clear if anyone signed it on July 4, 1776, except that it does appear that at least John Hancock and Charles Thomson did sign it then. The Declaration was not signed at one time in a single body of men. Once the Wording of the Declaration was agreed upon, it was handwritten and given to a printer. That version was signed by Hancock and Thomson. On July 19, 1776, Congress ordered that the document be "engrossed" and signed by all members of Congress. The engrossed document, the one on display in the National Archives, was not ready until August 2, 1776, when most members signed it. Several members were not there at the time and signed on various days afterward.