Thanks for professionally confirming the identity of the metal your 4-hole button is made of -- which turns out to be Zinc. As I mentioned in my previous reply, the US Army used zinc 4-hole buttons (on Army uniform pants) in the World War One era. You can recognize those because the larger ones have "U.S.*ARMY*" on them in raised letters, and the smaller ones say simply "*U.S.A.*" in raised letters. (See the photos posted below, including the dated label on the uniform's pants.) Your zinc 4-hole button still has a lot of crud-concretion on it. You might want to do some gentle scraping to see if it has any lettering (either raised or indented).
I do not know when ZINC 4-hole buttons were first manufactured. All I can say is that I've never heard of any being found in the BOTTOM of a civil war army camp hut-hole or battle-trench. "Surface" finds (meaning, found in the topsoil layer of the ground) cannot be relied on, due to post-civil-war junk commonly littering civil war sites. So, I would estimate your zinc 4-hole button being from the latter-1800s at the earliest, or the first half of the 20th Century.
Please let us know if your 4-hole button turns out to have any kind of lettering on it.