Your 1-piece cast pewter United States Infantry button is shown in the book "Record Of American Uniform And Historical Buttons With Supplement" by Alphaeus H. Albert as button #GI-41B on page 24, with info on page 25. The book describes it as "[US] Infantry, 1-piece convex pewter with iron shank. Device [meaning emblem], an eagle, a five-pointed star in an oval, UNITED STATES INFANTRY encircling, the star with short points."
It is quite rare. Congratulations!