What should I do to convince my family to approve my marriage to a young man who is well-off, religious, and of good character, but they reject him because his father works as a doorman? And is it permissible to marry him without their approval?

The guardian and witnesses are required for marriage. A girl's marriage is not valid without her guardian's permission. The compatibility considered in marriage is righteousness and good character. It is not permissible for the guardian to reject a committed suitor. The questioner is advised to try to persuade her guardian through prayer and seeking help from people of virtue. If he is not convinced, she may refer the matter to the Sharia court. If she prioritizes her parents' رضا (pleasure/satisfaction) and foregoes marrying him, she may find blessings in marrying someone better than him.