How do you get sponsored in shooting sports?
There are many paths to explore. The National Rifle Association
(NRA) has many options that you can explore online. That was one of
it's founding principles, to teach firearm safety and proficiency.
Then there is the International Defensive Pistol Association
(IDPA), the International Practical Shooting Confederation (IPSC),
and many smaller organizations like the American Action Shooting
Association (AASA).
Those also use shotguns and rifles, but if you are shotgun
focused try National Skeet Shooting Association · National Sporting
Clays Association for that.
Additionally, there are many businesses that teach hunting,
tactical weapon use, gunsmiths, ammunition production, et cetera.
Keep it safe, learn, practice often.