I think it doesn't matter where you are/how you start. I learned by having my first job at a startup (on a 1 year CPT stint btw, so yeah, you can weave things into the path to green cards/citizenship), but I don't think that's necessary or sufficient. It was useful in learning some superficial parts of the process, but what I learned most was about myself, and it was a kind of learning that I think could have come out of other experiences.

If you've got entrepreneurial instincts, you'll find a way to be entrepreneurial anywhere. Inside a big company, they like to call it "intrapreneurship." That's what I am up to right now. Any kind of *preneurship is a creative path, so you need to be creative even about the decision about how to GET on that path. They say Indonesia is hot right now, why not go there and do a contract assignment for a bit to see what's going on? Perhaps put your H1B plans on hold and work in Europe or China for a bit? Or work delivering pizza and consulting on WordPress on the side. If you think there's a set formula for becoming entrepreneurial, that's already a sign of formulaic thinking that will cause you trouble later.

The specific rituals may differ (getting executive sponsorship for a side project from some VP instead of money from a VC), and people may demand different sorts of proof for supporting you in different ways. But there's ways to challenge the status quo and make life interesting for yourself and everyone around you, no matter where you are. That's the soul of entrepreneurship I believe.

If you specifically want to be an entrepreneur of a particular type (example, standard-storyline valley startup born in Y-combinator, following lean startup theology) you have to go through that particular channel.

There are some who believe that entrepreneurship is a teachable trait and others who believe it is an inborn trait. The "teachable" camp obviously tries to teach it.

I think you can only learn the rituals/processes of a particular "school" (in the sense of artistic tradition), but not the basic attitude, risk-taking mentality, imagination, grit etc.To bring those parts of your personality out, you have to go through your own formative experiences, and they may come from very unexpected sources.

H1B/Green Card... yeah, get those out of the way, but don't hold up your interests for those things. Find a way to keep being entrepreneurial while doing that stuff, but if a chance comes up to be entrepreneurial in an exciting way by breaking the H1B path (thought experiment: the Singapore government offers great breaks to startups that set up shop there... would you consider that? You should be willing to).

Diving straight into a startup might give you the exposure to the process early, but OTOH, spending time in a low-effort cubicle maze figuring yourself out can be just as valuable to a later entrepreneurial venture. A stint at a big company might also expose you to opportunities, contacts and future customers, and problems the big company is solving badly that you could solve better on your own.

Maybe the best way to challenge yourself is to go in the direction of greatest uncertainty. You'll "fail fast" and learn if you've got *preneurial DNA real fast, by seeing if you can thrive in the uncertainty, or whether you were merely attracted to the idea of making it rich.