I believe what you are referring to is considered "passive income." This means that you can own shares or units of interest in an LLC, but cannot be an employee or active member of the company. So taking on a role as officer is likley going to be very problematic. You would be prohibited from managing or operating the business. For example, not being allowed to sign contracts.
While you can certainly create the entity and own it even though all owners are foreign residents, by virtue of being an owner does not entitle you to work, reside in or enter the US.
I think you should first discuss the limits of what you can do with an immigration attorney ( I have a referral for you if you like) then contact a business lawyer like myself to discuss the best entity options.
Most of us here, including myself, offer a free phone consult.
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