Stall & Dean patented a mitt in 1901 that included a cleft between the thumb and body to form a deep pocket. The cleft was then sewn together and encircled with a full perimeter banding.
I found this ad from 1903 showing such a mitt below.
The example below seems to fit the bill for such a design. A dart was cut into the face, stitched together to form a pocket and then fully banded.
Various patents continued until 1910. Below are three. Harry Decker patented this thumbless design in 1906 while incarcerated at San Quentin. One of the prison guards did the legal paperwork and was credited as a co-inventor. The mitt was a complicated mash-up of a removable glove section, the use of an air bladder and regular padding.
The 1906 patent of Raoul Le Mat featured a mitt with a rigid paper mache frame to which the front and back of the mitt are attached.
This last mitt was patented in 1910 by Samuel Waring. It include a prominent heel pad and a riveted leather finger guard/stiffener at the top.
I found a few old player/team photos that seem to show some sort of full round mitt.
Circa 1910
1900's
1900's