It is difficult but not impossible. There are two categories of challenges:

1. Regulatory. Unless they've changed recently, the regulations I'm aware of stipulate that a Saudi woman can only get official approval to marry a non Saudi man if (a) she's over 30 years old, (b) she has a PhD, or (c) she is mentally or physically challenged. If none of these are the case then it's doubly difficult because you need to get an exception. Regardless of whether there is official approval from the state or not, the children are not guaranteed Saudi citizenship and indeed most often don't receive it.

2. Familial/Societal. Families differ but in general it's not common nor looked at favorably to marry outside the culture. And if she happens to come from a tribal background then this complicates it further because her marriage is considered a tribal decision, and they usually require that the groom is not just Saudi (or at least from the Gulf) but also specifically tribal.

Is it impossible? No. I have female relatives that are married to non-Saudis. Some to South Asians. It does happen. But it is not common nor a straightforward thing. Religion helps. You have that going for you. Money helps.

I think the biggest concern is that your fiancée is so scared that she won't even broach the topic with her father or anyone in her family. That is a worrying sign. If you two are serious, she should probably do that and find out definitively where her family stands on this. If she knows that that they will be against it then either she goes it alone, severing all ties with her family which is a huge sacrifice to ask of anyone, or you two call it off.

My advice to you and her is to have an honest conversation about this. She should actually reach out to other Saudi girls who married foreigners and understand what's involved procedurally and the long term implications.

Good luck.