I have gone through with my own son so I feel comfortable in answering this question for you. The best way to catch on with a sponsor is by qualifying and entering some big competitions. Almost every ski resort at some time has some kind of skiing event, such as a Big Air comp, Half Pipe, Slopestyle, Bump Competition, etc. The bigger the resort, the more exposure you'll get. Alot of these events are sponsored by ski equipment reps who sometimes judge the events or have tents with displays for their goods.
Since you've got to start somewhere, check with your local resort and find out if and when they might have some comps. If you're good enough to make an empression and finish high up, then travel to some others, etc. The more exposure you get, the more wins or top three finishes you have under your belt will get you noticed. If you are real good, they will seek you out, they will know who you are. If this doesn't happen, you may have to start the ball rolling by making some phone calls or writing some letters. Then there's image. If they are going to put money and hard goods on the line to you, they will want you to hold up your end by showing an image to the rest of the ski world that you deserve what they give you and act appropriately, not being a jerk or worse. After all, you will be a spoksperson for them whether you know it or not.
There's alot to the game. My Son's college roomate is sponsored by Head, Smith, Scott and a few others. He got his first sponsor when he was 17. He is very good but as good as he is, he doesn't always qualify for the big Comps. His last chance was last weekend at the US Freeskiing Open in Vail. His first run in the Super Pipe Comp, he blew his ACL and MCL. Done for the year.
So, it can be done. Hope I helped you some. Good Luck