It's there a path into management without being a developer first?
1. Become a domain expert and work in the domain and then move into product management. Kind of a round-about way to go about it, but if you like the domain then why not.
2. There are also a lot of low level project coordination jobs out there. It's not really management and it's really stressful work as you get a lot of responsibility, but not a lot of power. But if you don't burn out then you'll slowly get more and more clout and move up the hierarchy.
Keep trying.
Hmm....