Is it permissible for me to have the dowry contract written by a state-affiliated notary, given that the ruler is the guardian of one who has no guardian, in the event that the girl's father refuses to marry her to me despite her consent and the consent of her paternal uncles and brothers, and his preference for another person who is less religious and of lesser character than me?

If the girl's father prevents her marriage to a suitable suitor, he is considered to be unjustly withholding consent (عاضل), and an attempt can be made to convince him. If he insists on refusing, the girl should refer the matter to the competent authorities, and the judge will marry her off or appoint someone to do so. If marriage can be facilitated through legitimate Islamic channels, then praise be to Allah. Otherwise, seek someone else and sever ties with her. A guardian should not marry his daughter to someone who is not committed to the Sharia (definition), especially one who abandons prayer, and a believing woman should not accept such a person.