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Repeat: totally legal to show up at a valid point of entry and request asylum
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Aside from asylum, there are three ways to “get in line” for citizenship in the USA: family sponsor, employer sponsor, and diversity lottery.
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Employer sponsorship is generally limited to those w special skills or those planning to invest a lot of $$.
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So, if you don’t fall into any of those categories, but you can make a credible asylum claim, that’s what you do.
If you can’t make an asylum claim, there’s no line to get in.