With one exception, my post Marriage marketing for Christians was ungendered, because I think the principles there apply to both sexes.
This was the exceptional paragraph:
If you're a man looking for a woman to marry, you or your broker contacting her father is the most biblically correct first step, though depending on her family situation that may not be possible or appropriate.
This is based on my reading/remembering of two passages:
If a man entices a virgin who isn’t pledged to be married, and lies with her, he shall surely pay a dowry for her to be his wife.
If her father utterly refuses to give her to him, he shall pay money according to the dowry of virgins.
i.e. if you get a girl to have sex with you and you're discovered, you have to marry her... except her father can still veto the marriage.
Also, when a woman vows a vow to Yahweh and binds herself by a pledge, being in her father’s house, in her youth, and her father hears her vow and her pledge with which she has bound her soul, and her father says nothing to her, then all her vows shall stand, and every pledge with which she has bound her soul shall stand.
But if her father forbids her in the day that he hears, none of her vows or of her pledges with which she has bound her soul, shall stand. Yahweh will forgive her, because her father has forbidden her.
i.e. in general, a father gets the opportunity to veto his daughter's vows when he hears about them.
This implies responsibility for/authority over a daughter becoming legally bound to a man in marriage.
But what if he's an idiot?
Famously, you don't have to prove competence to become a father. Not every man will be a good legal representative of his daughters, but it's still his role by default.
The father's default role notwithstanding, that Numbers passage has some qualifiers – this command is for a woman still in her father's household, specifically one who is young. I don't think you're required to go through the dad to marry a woman living on her own, though depending on her relationship with her father she might still appreciate having him in the loop or using him as a first-contact method.
Her dad may just not even be interested in getting involved. If he gives you a blank look and a shrug when you ask to talk to his daughter about exploring marriage, you probably don't need to make a big deal about asking
his blessing him not to veto your marriage vows.
But if she's living in her father's household, you should probably be involving her father. At the very least, she probably appreciates the chance to let her dad deliver a "uh, no"/"eh, maybe" message instead of having to tell you directly.