Just for those interested, the problems in Washington are unique to that state. There is no national requirement to restricting gun ownership to citizens, except for the following:
You must be a resident of that state for 90 days;
you must intend to live there permanently;
you must be a legally residing in the United States;
you must meet all other guidelines for gun ownership that citizens must meet and;
you must meet any additional requirements of the state you live in.
This is taken from the BATF website. The problem with Washington is the last line. They require an alien firearms license. Most other states don't. For instance California only requires proof of residency for 90 days.
Since it's a requirement of the state you live in, you need to be there for 90 days, prove it, then deal with their extra requirements.
There is nothing in our national laws prohibiting ownership by aliens except the residency requirements, the legal entry and visa, and it can't be a nonimmigrant visa (you have to intend to live here permanently).