Is it permissible to marry an adult woman without the knowledge of her family, due to their prior rejection and to avoid falling into sin, knowing that there was a previous relationship between the two parties and that the family was aware of it?

You must immediately cut off your relationship with this girl and repent to Allah for this relationship and the sins committed, for a Muslim loves for his brother what he loves for himself and dislikes for him what he dislikes for himself. Marriage without a wali (guardian) is not valid, and since the girl's wali has rejected you, you must seek someone else. You will find better than her, among those who do not engage in suspicious relationships. Be keen to marry a woman of deen (religious commitment).