The answer is “No”. As a H1-B visa holder you can start a business with an American counterpart but you will not be able to self-sponsor a H1- B or a Green Card. A H1-B is a work visa and it is sponsored by an employer, at the same time an individual cannot act as an employer and as an employee.

One of the many ways an Individual can obtain a Green Card is my investing over 1 Million US dollars through an EB-5 visa. The respective individuals should be able to prove he or she can create jobs for American citizens through their investment to obtain the Green Card. But, merely starting a company with an American citizen for few thousand dollars and sponsoring a GC for yourself is not legal