Banking in UAE for non residents (companies or individuals) is extremely difficult. Hardly you will find any bank that under normal circumstances will onboard you.
If you have a real use case of why you need an offshore company and you cannot work with onshore company and you are managing a lot of money, try to find a smaller bank where you can more easily talk with managers or branch directors to expose your case tell them the amount of money or business you will bring to them and you might be lucky, as smaller banks have targets to meet and you can help them︀ achieve them. But remember that this is case by case and you have to be︁ very lucky by meeting the right person at the right moment.
Other than that, go︂ the traditional onshore way and you will have bank easier (still can be hard sometimes︃ but easier than offshore)