Is it permissible for me to try to convince a girl who does not wear the hijab to wear it before proposing to her, or is that considered forbidden because she is not yet my wife?

One must lower their gaze, as Allah Almighty says: "Tell the believing men to lower their gaze and guard their private parts. That is purer for them. Indeed, Allah is acquainted with what they do." And as the Prophet, peace and blessings be upon him, said: "Do not follow a glance with another glance, for you are allowed the first, but not the second." To find a wife, it is recommended to seek a woman of religious commitment and intellect through one's mother or mahrams. It is permissible to look at the woman one intends to propose to if he has made up his mind to propose, as the Prophet, peace and blessings be upon him, said: "If Allah puts in a man's heart the desire to propose to a woman, there is no harm in him looking at her," and "If one of you proposes to a woman, there is no blame upon him for looking at her, if he only looks at her for the purpose of proposing."