Hey man. I'm an introvert. I don't consider it a problem. It just means my game will look a bit different than the extroverted guys.
To start a convo, try this: walk up to her and say "hey what's going on?" as if she's a friend you're bumping into. You're confident now, so you shouldn't have a problem with this. That will usually lead to an organic conversation, or if she's not feeling it you'll detect that and eject.
Remember that introversion refers more to how your energy works and less about being social or awkward. Large groups exhaust me so I typically won't perform well picking up at a club or whatever. But I do well at coffee shops or if I happen to start chatting someone up one on one at an event.
I think extroverts will always get more girls, because social interactions energize them (where as they drain introverts) so they have no problem boldly running up to a girl whenever, wherever. But the girls that I do meet I usually have a very, very high conversion rate with because, as is typical of the introvert, I give so much if myself to interactions with people so girls feel like they've had a real high quality interaction with me - which leads to dates which leads to sex.
Extroverts take energy from people, that's why they like hanging in groups. So whereas some girls will be approached by an extrovert and go, "ugh, I just so don't have the energy for this guy right now" I will almost never encounter that, because people instinctively get that I'm a relaxing presence and, if anything, can give them a boost.