Oil company----->MBB or Top uni--->MBB

So basically I have to make a choice right now: either go to the top university in my country (KSA) and try to break into MBB (the problem is I will be competing with other candidates that studied at top universities worldwide since my country sends a lot of students abroad and pays for it) or I can go with Saudi Aramco (the biggest oil company in the world and highly respected in the region). They will pay for all my university expenses (at a t30 university in finance) and give me a generous stipend during my university years, reaching 4000$/3000 pounds if I live in big cities like NYC or London, respectively, unlike the ministry of education, which gives you 1700$ no matter where you go. The catch is if I go with Aramco, I will have to work for them for 4 years after I graduate. Will this screw my chances of getting into MBB since most consultants will be getting their MBAs at this time and will have a great experience in the consulting space, unlike me, who spent 4 years in industry/corporate finance role?Or it is fine I just have to get my MBA and I should be able to recruit to post MBA roles.

Any feedback would be helpful and thanks everyone