That sounds more like the process of applying for a Labor Certificate, as part of a green card. For an H-1B you just need an approved Labor Condition Applicatio

That sounds more like the process of applying for a Labor Certificate, as part of a green card. For an H-1B you just need an approved Labor Condition Application, which attests that you're offering the "prevailing wage" for the region/occupation, and (I think) that there's a general shortage of that occupation in the region (and not that you had no US citizen replies to your specific job advert)