What should a girl do who regrets a sin and transgression she committed, as she had a previous relationship with a young man before engagement, and wants God to be pleased with her?

What you mentioned about your relationship with that young man is considered a sin that requires repentance. Relationships between the sexes outside of a lawful marriage are forbidden and lead to corruption. Speaking between a non-mahram man and woman is not permissible except out of necessity and with Islamic regulations. Allah the Almighty said: "And when you ask [his wives] for something, ask them from behind a partition. That is purer for your hearts and their hearts." He also said: "Then do not be soft in speech [to men], lest he in whose heart is disease should covet, but speak with appropriate words." Your intense regret is a good start for repentance. The conditions for repentance are to abandon the sin, regret it, and resolve not to return to it. The one who repents from a sin is like one who has no sin.