Most of my first contracts happened because of other developers I know recommending me to someone.
After that, the customers started recommending me to their friends.
Hang in there, and make sure that everyone you know is aware that you are available.
Again, DON'T SELL YOURSELF. No one cares. Tell the person you're taking to about themself. Tell them what you like and love about them, and then tell them how you'd like to help them, and what an honor it would be, and how much you expect to learn. Let them know you're doing it for a very selfish reason - so that you can learn from them.
It's key you legitimately respect whoever it is, because you'll sound empty if not, and you are going to make a million mistakes that are very obvious in hindsight. So find someone you really respect, and talk about them (not yourself - no one cares, really), and then make damn sure they know they're getting 130% effort for 30% price or so. The lessons and reference from someone you respect are going to be worth a heck of a lot more than whatever you could get by trying to over-represent yourself to an unsophisticated buyer.
To work with someone very talented, they'll want to know that you're mentally and emotionally onboard and very excited to work with them personally, and that your effort will make up for your inexperience. The enthusiasm is what gets them willing to give you a chance, the undermarket rates is what gets you the contract. Later on, you can raise your rates, but do try to make the first person you get someone you really admire - bad clients are really a nightmare, and you'll have to deal with that later, but good clients are like mana from heaven. Do what you can to get people you really truly, deeply respect for your first gigs, even if it's a bit less than you could get on the open market. It'll be very worth it in the long run.