How can a young man's desire to marry a girl with whom he made a mistake be reconciled with his parents' desire to reject this marriage?

Attachment to a non-mahram woman, being alone with her, looking at her, and deriving pleasure from her body are all forbidden, based on the words of Allah Almighty: "Tell the believing men to reduce [some] of their vision and guard their private parts," and the saying of the Prophet, peace and blessings be upon him: "No man should be alone with a woman unless there is a mahram with her," and "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman who is unlawful to him."

You must repent and cut off the relationship with the girl. If she agreed to these sins, then she is not religious, and it is better not to marry her, based on the saying of the Prophet, peace and blessings be upon him: "So, gain success with the religious woman, may your hands be dusted with dust." This will please the parents. Marriage to her is not valid except through her guardian.