'2' would be a Regiment number
If the second letter on the cartridge box is a 'J' (as in NJ), then that'd indicate
History of the Second New Jersey Infantry Regiment in the American Civil War with timeline of important events, movements and battles.
civilwarintheeast.com
The gear is for a percussion weapon (note the cap box), so it's not for the 2nd NJ of the Revolutionary War.
If the bayonet fits one of the weapon types issued to the 2nd NJ, you've got more proof.