When reaching out to an unknown girl to potentially become friends, it's essential to approach the situation with respect, kindness, and sincerity. Here's a friendly and respectful first message that you can consider sending:
"Hi there! I hope this message finds you well. I noticed we share some mutual interests or friends (if applicable) and thought it'd be great to connect. I'm always open to making new friends and getting to know awesome people. If you're interested, I'd love to chat and learn more about your interests and experiences. No pressure, though! Have a fantastic day!"
Remember to be polite, genuine, and considerate of her time and boundaries. Avoid coming on too strong, and be patient as building a friendship takes time. Respect her response, and if she doesn't seem interested in connecting at the moment, don't take it personally and move on gracefully. Good luck!