I am the Product Manager at my company.
We are a dealer, distributor & service depot for scientific and industrial equipment and so I’m not sure how relevant this is to the OP’s question.
While I do have a BS, I think I could have got here without it given my fairly long and successful 12 year history with my employer. Hard to say since it’s difficult to separate skills and knowledge gained during college vs elsewhere. I was initially hired after I dropped out of college but I worked a few years, took a few years off to finish school and came back against all vows.
My background is engineering rather than sales but I realize that this is unusual and it must be said that I’m a poor engineering student and can’t pretend otherwise with the honor-rollers. Personality goes a long way but it may be hard to get started cold without what many consider a minimum education level. Certainly, you’d need some pretty excellent experience to get noticed.