I'm not a recruiter but we tried to hire someone who needed an H1-B/J1 visa and it was truly awful. We went through trying to make it work/expedite the process but there was nothing to be done. He was awarded the visa and we would have still had to wait another 4 or 5 months till they could actually start.

I'm usually quite proud of the United States but it was baffling to me how challenging this was. We have a highly qualified person, who has an employer looking to pay them, of which they will have taxes going to the United States, you've already vetted them as being okay, and yet it's still going to take nearly half a year for you to allow them to come work here.

It makes me wonder what the hell people do all everyday at the government.

To answer your question, I don't think anyone, especially a recrutier, can make the process easier.