I guess the bottomline is that you can start and invest in a company, but not work for it.
Have you already applied for a Green Card? While you wait, maybe you could invest your free time now in an open source project that you could potentially leverage for-profit services later on, after you get your GC.
Another thing you could do while you wait for your GC is to simply start a savings account and accumulate a little bit every month, so when you get your GC you have enough funds to start a company and survive without a salary for a while (I'd recommend 1 year of living expenses).
Another option is to go get some higher education, which you can do as a H1 / work visa. Because you work for a large company, they probably offer tuition reimbursement programs. Take advantage of those programs as much as you can!
In short, use the time between now and your GC to prepare yourself and your life to eventually start a company. I'm now a GC holder, but I have immigrated to US via a work visa as well... So I understand your frustration, but I don't think you have many options, unfortunately.
Close, but not quite (according to the immigration lawyer I used). You can start a company. You can invest in it. You can even work for the company. But you cannot pay yourself any money for that work. Any work you do for the company must be gratis.
So you need an alternative source of income, as well as a reason to legally stay in the US. Usually these both come from a job, which will of course get in the way of your startup efforts!
If a co-founder or a board-member of your company is a US citizen, they can theoretically sponsor an H1 transfer providing you already have an H1. In practice this is difficult and time consuming.
I opted to wait for the GC...
How did you guys do it? I'd so greatly appreciate any advice. I already am in the US, working for a large company (on a work visa)