At the match game of Base Ball played at Litchfield, August 30, 1866, between the "Prairie" of Litchfield and the "Active" of Alton, the following was the score...(Prairie 64, Active 36)...
The "Prairie" Club victorious by 28 runs. Time of game three hours and forty-five minutes. Umpire, E.L. Metcalf. Scorer E.T. Atwood.
Baldwin field captain of "Active" club, Forrester field captain "Prairie" club.
-Alton Telegraph, September 7, 1866
Playing for the Active Club was Baldwin, c; Perrin, 1b; Sioman, cf; Morrison, 2b; Kellenberger, 3b; Dobelbower, rf; Clement, p; Smith, ss; Schweppe, lf.
In all honesty, I wouldn't be surprised to find evidence of east-side clubs in the summer of 1865, after the war ended, but 1866 makes a lot of sense. The war was over, the game was exploding in popularity and lots of new clubs were being formed. Most of the first clubs that we know of for any given city in the Midwest were formed in this post-war era.
Talking specifically about the St. Louis area, the Empire Club had a great deal of success in 1865, claiming the mythical Championship of the West, and that success most likely played a role in increasing the popularity of the game and the creation of new clubs in the area. Alton also had a rich ball-playing tradition that dated back to the antebellum era and it's not surprising that the first club on the east-side would pop up there.