as usual there is as much mis-information as information provided here.
There is, of course, no answer, because if you care to check the successful Broadway producers you will see that there are as many paths as there are people. Business school, law school, drama school, no school-all can work. (And by the way there are courses in producing both academic (e.g., Columbia) and non-academic (e.g., the Commercial Theatre Institute).
If you show up with enough money, it doesn't matter where it comes from. But the primary task in theatre is almost always the same: meet as many people as you can, and find opportunities to work with first rate people no matter what you are doing. And absorb everything. If you have billions, you still need to learn everything you can before you try calling yourself a producer, unless you want to be like the rich people we make fun of here,
Once you follow whatever path you follow educating yourself, you want to get in with the real players if you can. Most often that means going to work for a GM or a producer and focusing on being nice to be around (usually!), upwardly mobile and smart. But there are highly successful producers who started lots of other places-agencies, press offices,booking offices, law firms, even on the creative side. The key is what I said before-keep yourself in the mix. Learning to network without being obnoxious is probably the single most important skill you can learn. Unfortunately, it isn't always a learnable skill. Oh and luck helps. I wish you that.