Who was quarterback in first NFL game?

I do not know the team schedules for 1922. Perhaps this will help your research. 1922 The American Professional Football Association changed its name to the National Football League, June 24. The Chicago Staleys became the Chicago Bears. The NFL fielded 18 teams, including the new Oorang Indians of Marion, Ohio, an all-Indian team featuring Thorpe, Joe Guyon, and Pete Calac, and sponsored by the Oorang dog kennels. Canton Bulldogs 10 0 2 1.000 Chicago Bears 9 3 0 .750 Chicago Cardinals 8 3 0 .727 Toledo Maroons 5 2 2 .714 Rock Island Independents 4 2 1 .667 Racine Legion 6 4 1 .600 Dayton Triangles 4 3 1 .571 Green Bay Packers 4 3 3 .571 Buffalo All-Americans 5 4 1 .556 Akron Pros 3 5 2 .375 Milwaukee Badgers 2 4 3 .333 Oorang Indians 3 6 0 .333 Minneapolis Marines 1 3 0 .250 Louisville Brecks 1 3 0 .250 Evansville Crimson Giants 0 3 0 .000 Rochester Jeffersons 0 4 1 .000 Hammond Pros 0 5 1 .000 Columbus Panhandles 0 8 0 .000 ----
The precursor to the NFL was the American Professional Football Association which played 1920-1921 before changing its name to the National Football League. The first game played in the APFA in 1920 was between the Dayton Triangles and the Columbus Panhandles. The position of quarterback had not really been defined at that time. Most offensive plays were running plays run from the shotgun and the passing game was not used very often. Whatever back took the snap from center was capable of throwing a pass. For the 1920 season, players on the Dayton team credited with throwing passes were Al Mahrt, Frank Bacon, Dick Abrell, and George Roudebush. The four threw a combined 88 passes in eight games in the 1920 season. Only one player for Columbus was credited with throwing a pass in the 1920 season, Frank Nesser. Nesser threw six passes in five games. I guess anyone of the above five players could be considered the first quarterback.