How can i help my boyfriend get his residence or work permit?

We have been dating for a while and for the longest time he has been going on living life without an ID. It is really hard just due to the fact that the only "valid" identification is his Chilean ID that he recently got from the Chile Embassy here in the US. My boyfriend came into the US with his "parents" back in 1992, he was 3 years old. With recent events turns out he was adopted in Chile when he was two months old. His real mom couldnt afford to take care of him, and he never knew who his dad was. So the birth mom gave him away to a family she knew, he would be safe with. No real paperwork was ever recorded on the adoption. The whole family came to US on visitors visa, in the end they liked it here and stayed. Everyone in their family has the same last name, except my boyfriend. His family now are all residents, except for him. He could have been included but wouldnt have worked since his last name is completely different. Now he's stuck trying to be a good citizen, he still pays taxes, and all of that but in all reality he is still illegal, we ended up meeting eachother and now are planning to get married. What ways should I go about this ordeal? Should I try to get him a green card? Just a work permit?