How can I convince my family to approve my marriage to a committed girl, given their refusal on the pretext of current financial inability, and my desire not to disobey them?

Marriage is recommended for those who can afford it and have a strong need for it. It becomes obligatory if one fears falling into sin, and abandoning an obligation is a sin. There is no obedience to a creature in disobedience to the Creator.

Parents should assist their child in getting married, as it is a protection for the soul, a source of comfort, and tranquility. Early marriage is not a problem; rather, it is a helpful factor. If financial difficulties are the impediment, Allah has promised to enrich those who seek chastity from His bounty: "If they should be poor, Allah will enrich them from His bounty." And there are three whom Allah has a right to assist: one of them is the one who marries seeking chastity.

The questioner should adhere to chastity, fast, and occupy their time with beneficial activities. For whoever seeks chastity, Allah will grant it to him. Fasting is a protection for those who cannot afford to marry.