As you're aware, minor leagues existed before 1903. Formal farm systems didn't start until the 1920s, but teams had long had informal working arrangements with minor league teams. Many of those arrangements were, technically, outlawed pursuant to the National Agreement, but teams employed many ingenious ways to skirt the regulations.
You may want to try creating independent minor leagues - i.e. leagues where the teams have no affiliations with major-league clubs. OOTP has made some strides in this area in the latest version, and there have been some recent discussions regarding the best way to handle independent leagues (see, e.g.,
here).