There's a catch-22 here. They won't want to see you if they don't know you and they can't know you if they don't get to see you.

Solution: Create your own gigs and start small. House concerts. Find a friend with a large enough space or make one yourself.

Libraries, museums and schools are a good contact if you know someone there.

Play various places...even volunteer sometimes...because they will see you and maybe hire you later. (Don't overexpose self for freebees, however).

Start promoting yourself with people you already know. Play parties (birthday, theme etc.)
Don't overprice yourself.

Keep working at your craft. Sometimes in that process, contacts are made through your teachers, and other support-networks.

At first, don't bother with coffee-houses, restaurants or clubs. The first are too crowded and you generally will not show up well because there are time restrictions and often erratic time-slots. Restaurants generally can't afford you today. Clubs are the worst.
Alcohol and attention to folk music doesn't work well.

Frank Hamilton