Does marrying an unveiled woman contradict the Prophet's (PBUH) saying: "So win the one who is religious, and you will prosper," given the husband's intention that the wife will commit and wear the hijab at his hands?

Do not marry a girl who insists on not wearing the hijab, because she is disobedient and cannot be trusted. However, if she expresses her full readiness to commit after marriage, and you are strongly confident that her situation will change for the better towards righteousness and uprightness, then it is permissible to marry her. This might even be commendable, as you would be a reason for her adherence to religious practice, fulfilling the Prophet's (peace and blessings be upon him) saying to Ali: "For Allah to guide a single man through you is better for you than having red camels."