Absolutely. There is no residence requirement or immigration status required to legally start a company in the US. I have addressed this on my law firm's blog: http://www.meltzerhellrung.com/blog/can-foreign-students-and-other-immigrants-start-businesses-in-the-us/

In terms of getting to the US once you have decided to open your business, that would depend on a variety of factors. I recommend contacting me directly to discuss your situation further. I would be happy to discuss what immigration options you may have as an entrepreneur.

Can you do it? Yes, absolutely. Is it simple and/or easy? Unfortunately not.

If you're going to go down this route then be prepared to spend a fair bit of money on legal advice, as well as budget in at least 3-6 months for the whole process. And don't be a cheapskate either - one wrong move can jeopardise all of your efforts.

On that note, you will soon find out that getting a company registered in the US will be the least of your worries, but what will prove difficult is getting any sort of banking set up for the company, as banks nowadays have extremely rigorous due diligence requirements in place and they're generally very hesitant to open accounts without you being physically present.

The best advice that I can give you though is to first get started with executing your idea - and if it's any good and properly validated then needing to establish a presence in the US will be a good problem to have.

I have founded two startups in the US. I am an American citizen but living abroad and I know other people who have set up US based companies even if they are not citizens. I know some companies that can help with all of the paperwork that needs to be filed.

If you would like to discuss how this is done, and if it is a good idea for your company, please feel free to contact me and schedule a call.