Is it permissible to speak with a girl to ascertain the possibility of marrying her after a silent love story, knowing that the intention is honorable?

You did well by not speaking to the girl, and you must protect your chastity, as she is a stranger to you. Marriage is the best solution for those who love each other, and it is permissible to inform her of your desire to marry while adhering to Islamic guidelines. However, it is better to seek the help of one of your trustworthy female relatives to avoid the devil's pretexts and to spare the girl embarrassment. If the marriage takes place, then praise be to Allah; otherwise, turn your heart away from her. Remember that a good intention does not make a bad deed good.