What is the ruling on a girl going out with a young man with a sincere intention for marriage, knowing that she is religiously brought up and not easily deceived?

Islam does not permit any relationship between a man and a woman outside the framework of a legitimate marriage, due to the corrupting influences that result from it. The sincerity of the actor's intention does not make what is unlawful permissible. Uprightness necessitates abstaining from what the Sacred Law has forbidden. Therefore, it is not permissible for this girl to go out with this young man. If he truly desires to marry her, then he should propose to her through her family. Otherwise, it is obligatory to cut off the relationship between them, based on the Almighty's saying: ﴿O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing.﴾ [An-Nur: 21].