Military service doesn't necessarily have to involve fighting. And let's expand that to any kind of public service. They need to have some skin in the game. Stealing and forging identities, avoiding paying taxes, and going underground doesn't do that.

Welfare and public benefits should not be used for them. If Congress wants to create a separate fund then so be it. But it should be charged back to the nation of origin not taxpayers.

Sponsorship can come from community groups, family members, friend, employers or school. Very much like the Cuban Refugee program.

Foreign nationals should not be allowed to vote until they officially naturalize as a citizen. But for these people, it's a pathway that is going around the proper channels. If they can stick with this plan for 5 years, then they can be granted citizenship and vote.