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.