One thing I learned right away in relic digging is don't be surprised when you dig later period items in an early period spot because the area was visited or occupied beyond the first relics being lost there. I once dug on a Yankee picket point that overlooked the approach of a water way. I was digging civil war and Spanish American war era buttons. Turns out the same point was occupied by Federal troops during both periods because what is considered a tactical advantage point will continue to be reused.
Marine Corps buttons are very hard to pin down a date when the back of the button is missing since you no longer have a makers mark to go by, and even when you do the mark may give you a 30-50 year window as well.
I assumed the back had been brass as well. Could you post a side shot of the button from the side with the piece of back attached? Marine Corps 2 piece buttons started out high domed or puffy if you will. As time progressed the 2 piece buttons became thinner in appearance. If you have a high dome then I would guess late 1800s, but if it was a slim button then I would guess early 1900s.
I just realized that you have it next to a quarter which makes it very large and therefore I would place that early 1900s since I believe they were over coat buttons.