Move on. There are millions of fish in the sea and there is no good path from this point that puts the two of you on the equal footing you need at the beginning of relationship. Sometimes chemistry doesn’t click for someone and you can’t convince her it exists. If you think she said no for a reason, like you were a jerk or she thinks your values aren’t lined up, then you can apologize or rationalize, but you’ll still be starting out a half step behind where you want to be.
Ask yourself if you really want to go out with her again, or you just hate the idea that she doesn’t want to go out with you.
Walk away, and in three weeks if she’s still on your mind then we can talk again about strategies to get a second shot.