In terms of baseball, MLB has a couple minor leagues that were started after WWII.

Southern League (AA) - 1964
Midwest League (A) - 1947
South Atlantic League (A) - 1980
Northwest League (A short season) - 1955
Arizona League (Rookie League) - 1988
Gulf Coast League (Rookie League) - 1964
Dominican Summer League (Rookie League) - 1985
Arizona Fall League - 1992

Independent Leagues
American Association - 2005
Atlantic League of Professional Baseball - 1988
Canadian American Association of Professional Baseball - 2005
Empire Professional Baseball League - 2015
Frontier League - 1993

If MLB doesn't want the new collegiate pro baseball to be a minor league affiliation, then they could go the independent route.

In terms of basketball, they could always go the way of the Continental Basketball Association (ceased in 2009), Continental Basketball League (ceased in 2012), or the American Basketball Association 2.0 (founded in 1999 and still in operation).

Even football has other leagues besides the NFL; USFL, WLF, WLAF, XFL, and a bunch of semi-pro leagues. So what is 1 more attempt to start another outdoor league?