The answer to your question will be heavily influenced by what you want that office to accomplish. Do you merely want to have a USA-based address (so you do not appear "foreign")? Do you want to have people traveling to customer sites within the country? Do you want this office to handle support calls as well? Are you after getting sales, or also providing a service out of this office?
And yes, it is of course possible for a business person to set up an office or a business in the USA. People here don't want foreigners to take jobs away, but they welcome foreigners that come here to set up companies. It's strange: As a foreigner you can start a business here, but you cannot work in it. :-)
These are, of course, very generalized statements. You need to consult with an attorney to see exactly what your options are as a foreigner. There are special visas for people that come here to start businesses (that would allow you to work in the business you start), for example. You need legal advice from an expert because there are many conditions that you must satisfy, and things have to be done in certain order.
Anyway, I would figure out what you need to do from this office first (my first paragraph), and once you have a very good idea of what you need, I would worry about the legal aspects (should you incorporate, physical location, visas, permits, employees, etc...).
EDIT: Just one example of a way to get a US visa to come start a company (or satellite office): EB5 visa: A foreign national must invest at least $1 million in a US business and create full-time employment for at least 10 US workers. The investor must remain involved with the business for a two-year period before he will qualify for permanent resident status.
There are other ways to do it, so I strongly advise to consult an immigration attorney once you know what you need to do with your office.
EDIT2: I just realized that you never state you actually want to come here to open your office, so ignore the visa talk if it does not apply to you.