The button is smaller than a dime, as you can see in the picture. I found this at the bottom of a dam on the side of a hill next to a tree trunk where a 1 X 1 area of sand has been deposited during floods.
I agree that Steve in PA nailed it; Great Seal button, 1902 onwards. The soil really did a number on this one, but you will find much better ones soon. Keep it up.