You can apply for a green card at any time while on an H1B as it is a dual intent visa (i.e. they don't think its a problem if you tell them you want to stay permanently unlike E2). A shell company is highly unlikely to get an H1B petition approved
How quickly/successful you are with your GC application depends on whether you can qualify for EB2 or have to go through EB3. EB3 is backed up for years. EB2 is current (therefore around 12 months wait) if you are not from india and china but you need to have a masters or 5 years of provable experience (letters from previous employers) in an area that the petitioning company cannot find an American will the same skills.
The E-2 can be a bit of a trap IMHO. If your business fails or you sell it, you have to leave the US. This might seem reasonable until you consider someone might run a small company for years, build a family, settle, and then have to leave because of economic downturn or because they sell their company. I don't know how easy it would be for someone to move from owning/running a company under E-2 to H1B employee of a new owner.
tl;dr? There is no clear path from E-2 to green card.
How quickly/successful you are with your GC application depends on whether you can qualify for EB2 or have to go through EB3. EB3 is backed up for years. EB2 is current (therefore around 12 months wait) if you are not from india and china but you need to have a masters or 5 years of provable experience (letters from previous employers) in an area that the petitioning company cannot find an American will the same skills.
The E-2 can be a bit of a trap IMHO. If your business fails or you sell it, you have to leave the US. This might seem reasonable until you consider someone might run a small company for years, build a family, settle, and then have to leave because of economic downturn or because they sell their company. I don't know how easy it would be for someone to move from owning/running a company under E-2 to H1B employee of a new owner.
tl;dr? There is no clear path from E-2 to green card.