I'm a resident of Indiana as well as the US. I'm not a citizen yet. As far as I know according to the law, as a permenant resident I am allowed to buy and own guns. It's just visitors who aren't.
I'm not waiting three years to own guns (citizenship).
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Green-card holders and immigrant aliens who do not yet have their green card are both okay under federal law
Edit: I think I need to prove 90 days of residency in the US/state. Which I can do once I find my bank statements.
Non-Citizens can own guns. I have a Canadian friend who is a gun owner and resident of the US. He's working on getting his citizenship. Basically he's in the same legal category as you. Resident, non-visitor, non-citizen.