How do you smoothly proposition your girlfriend to make out with you for the first time?

The best way isn't to come right out and ask her. Girls like to be romanced, so take your time. Start out by holding her hand or put your arm around her. Take her to a romantic movie sometime, or just spend some quality time together having a nice heart-to-heart conversation. Spend some time just gazing into each others eyes and give her a few kisses on the hand or on her forehead or cheek. This will let you gauge how interested she is in making out with you. Just remember to not move too quickly! Let the emotions and tension build. If she seems to like your casual kisses, slowly move in, close your eyes, and kiss her on the lips. If she is interested, she will kiss back. If she pulls away, give it some more time... she might not be ready for it yet. Patience is very important. Don't give up! Good luck to ya mate!