Good and quite popular question. If you are aiming to be a pro in Disc Golf, you want to build your career from the bottom to the top. Sponsorships are one key part of that. I think all Disc Golf companies are looking for outgoing, nice and talented player who can represent the sport as well. I do not think there are minimum requirements set, but to be selected by Disc Golf company, you need to play bigger events. Try to attend the biggest events in your area. Most of the Disc manufacturers like to see that you really like to throw their discs. There are different levels of sponsorships. Some companies sponsor celebrities, ambassadors and TDs as well.
I wish good luck to you. Do not hesitate to write to your favourite manufacturer and tell them how much you like their stuff.