Mexican troops left Tucson on March 10, 1856. As historian John Bret Harte explained in his book "Tucson, Portrait of a Desert Pueblo," they stayed 21 months after the city officially became part of the United States because, well, "there had been no Anglo force to take their place." There still wasn't on that March day, but "nine Anglos pieced together ocotillo canes to make a flagpole and ran up Old Glory in what is now El Presidio Park," Bret Harte wrote.
It does not appear that the Fourth of July was much of a public event during our early years in the USA. The oldest reference I find in a newspaper is an 1871 account in the Arizona Weekly Citizen that describes how the holiday was "creditably celebrated" here. Guns were fired at Camp Lowell, the courthouse was adorned with flags and the Declaration of Independence was read.
Chief Justice John Titus gave a fine oration, the newspaper said, but "having been pressed into service the previous evening, the justice attempted no studied address." A brass and string band played "Yankee Doodle" and the whole affair wrapped up at about noon. "The assemblage dispersed, feeling that it was good to have been there, and better still to be an American Citizen."