What current branch of the US Military was a corps of only 50 soldiers when World War 1 broke out?

It did not exist.
The smallest US service branch was "officialy" established in 1915 as the US Coast Guard. It had long existed before then under other guises and
The Marine Corps, busy in Haiti at that time had a sizeable force spread
across the globe.
The Navy's fleet though small was able to "Show the Colors" around the
Army strength was terrible. Weapons, troops and equipment could hardly
field a division for deployment anywhere.
Oh! You must mean the US Air Force which did not exist until 1947. The
smidgen of Army Aviation may meet your criteria, but it wasn't a "corps'.
Like Naval Aviation, it was an experiment,