Where there's a will, there's a way...
If you have a degree, that's great, it makes it easier. Other than that, you can apply for recognition of prior learning. 3 years experience is equivalent to 1 year of a 4 year degree program. You'd therefore need 12 years experience or a combination of uni credits and experience.
It would not be inconceivable to use other skills in order to make your application for an H1b a specialist job. You'd need to use your imagination in combining your skills into a job which requires specialist knowledge but it can - and has been done. Whether that is appropriate in this situation - I couldn't say - but if they were willing to work with the applicant it is possible.