Various details help us to narrow down the date range of the jacket whose buttons you found.
1- US Army "Great Seal" buttons made prior to 1910 did not have a raised rim, Your buttons have the raised rim, so they cannot have been made any earlier than 1910.
2- US Army Great Seal buttons had what is called "black finish" on them from sometime before World War One until 1923. Your "rimmed" Great Seal buttons show no sign of the "black finish," so they are almost certainly from 1923-or-later.
3- The backmark on one of them says "Waterbury Button Co." That button-manufacturer changed its name to "Waterbury Companies" in 1943. (And therefore, the backmark changed from Co to Co's.) So, that button almost certainly was made sometime between 1923 and 1943.
4- After World War One ended (in 1918), the size of the US Army rapidly shrank very drastically, back down to its traditional small peacetime size... and thus, comparatively few US Army uniform buttons needed to be manufactured. The US Army stayed small until America entered World War Two, causing multi-millions of army uniforms to be made for the enlistees and draftees in 1942. So, the "numerical odds" greatly favor your buttons having been made during 1942 to 1943 (when the Waterbury Button Co. changed its name to Waterbury Companies Inc).
