I am not currently sponsored for various personal reasons. But I have gotten several offers, some from big name companies.
First, obviously I travel a lot and I play a lot of tournaments all around the country, people know who I am everywhere, and that gets noticed. Now I'm not saying you have to travel the country, but making an appearance at tournaments in different regions, especially but not limited to tourneys sponsored by your target company.
Secondly. Let yourself be known, introduce yourself to people, players, TD's, volunteers, thank them for the work they've done, be genuinely friendly.
Support the sport in a positive way: introduce new players, teach new players, return plastic, little things will be noticed. Be helpful, ask if the TD needs help, either setting up beforehand or tearing down after everyone else has gone. Fire up a grill and cook hot dogs for the lunch break. Volunteer for events, run a league, develop a program that spreads the DG word to children, etc. Word spreads about the positive roll model you are - the DG community is very small. Likewise, people will notice if you're a dick.
Sponsorship opportunities will find you.