The New York - Penn League is where my internet name comes from, in fact.
There are a few independent minor leagues, actually, but it is much harder to actually work your way into the majors through them.
Even if you get plucked out of the independent leagues, it usually just puts you into the higher affiliated minors to work your way through that again.
The progression through the affiliated minors (Rookie leagues - shortseason A - fullseason A - AA - AAA - majors) is generally the way to go.
In the low minors, even into the Eighties there were very rarely teams that are independent for one year or two while they were looking for affiliation if they were profitable enough to survive without an affiliation for a time but even then, they generally field teams of players contracted into major league systems that were just loaned to them for the season. It is almost unheard of these days, though.
Also, these days it is common for the major league team to own one or two of its minor league teams outright, generally a low-minors team that is geographically close to the parent club, for the purposes of cross-promotion and for ease of using the minor league teams for rehabilitation assignments for returning major leaguers from injury.
If your major league star needs to play in four or five games to get back into playing shape, why not own the single-A team an hour away from your city and keep the profits from the increased attendance to see the major league player in the minor league park, you know? Why not keep the profits from locals who don't wanna pay major league prices but wanna see pro baseball?
The Mets do this by owning their Brooklyn shortseason-A team, the Yankees do this with their Staten Island team, I think that the Red Sox own their Lowell, Mass team... I think that the Angels might own their Rancho Cucamonga team... and so on like that.
It is a little bit cynical but it maximizes the profits associated to owning a functional monopoly on high-level professional baseball.
I personally believe they're slitting their own throats because part of what developed baseball fans in smaller markets was minor league baseball in more rural markets but... I'm just Cassandra on this topic.