How can one atone for the sin of being alone with a young man and exchanging kisses with him, given the remorse and the termination of the relationship, and the desire to please Allah after becoming engaged to another young man?

What you did is forbidden (haram), and such practices are not permissible for a woman except with her husband.

You must cut off all ties with that young man permanently, repent, seek forgiveness, and fulfill the conditions of repentance.

If the kissing occurred during the daytime in Ramadan and led to the emission of semen, then you must make up that day, along with repentance and seeking forgiveness.

You should accept marriage from the suitor if he is religious and of good character. Beware of informing him of what happened with you previously, and conceal yourself with Allah's concealment.